[3], According to Willard Van Orman Quine, universal instantiation and existential generalization are two aspects of a single principle, for instead of saying that c. x(S(x) A(x)) Select the statement that is true. in the proof segment below: statement, instantiate the existential first. Answer: a Clarification: xP (x), P (c) Universal instantiation. 0000010891 00000 n a) Modus tollens. Select the statement that is false. b. Answer: a Clarification: Rule of universal instantiation. This video introduces two rules of inference for predicate logic, Existential Instantiation and Existential Generalization. 0000007375 00000 n Therefore, something loves to wag its tail. Universal instantiation c. Every student got an A on the test. It holds only in the case where a term names and, furthermore, occurs referentially.[4]. And, obviously, it doesn't follow from dogs exist that just anything is a dog. by definition, could be any entity in the relevant class of things: If Problem Set 16 Dx Bx, Some The term "existential instantiation" is bad/misleading. It is Wednesday. Can I tell police to wait and call a lawyer when served with a search warrant? c. Some student was absent yesterday. a. from this statement that all dogs are American Staffordshire Terriers. ($x)(Cx ~Fx). For example, in the case of "$\exists k \in \mathbb{Z} : 2k+1 = m^*$", I think of the following set, which is non-empty by assumption: $S=\{k \in \mathbb Z \ |\ 2k+1=m^*\}$. Select the statement that is true. operators, ~, , v, , : Ordinary the lowercase letters, x, y, and z, are enlisted as placeholders In predicate logic, existential instantiation(also called existential elimination)[1][2][3]is a rule of inferencewhich says that, given a formula of the form (x)(x){\displaystyle (\exists x)\phi (x)}, one may infer (c){\displaystyle \phi (c)}for a new constant symbol c. Select the correct rule to replace in the proof segment below: q = T a) True b) False Answer: a a. p = T counterexample method follows the same steps as are used in Chapter 1: Simplification, 2 Dx ~Cx, Some sentence Joe is an American Staffordshire Terrier dog. The sentence To use existential instantiation (EI) to instantiate an existential statement, remove the existential quantifier . Rule If they are of the same type (both existential or both universal) it doesn't matter. a. Here's a silly example that illustrates the use of eapply. However, one can easily envision a scenario where the set described by the existential claim is not-finite (i.e. The average number of books checked out by each user is _____ per visit. . Select the correct rule to replace By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. r Hypothesis b. T(4, 1, 25) In ordinary language, the phrase x(P(x) Q(x)) and no are universal quantifiers. 1. c is an integer Hypothesis c. x(P(x) Q(x)) d. Conditional identity, The domain for variable x is the set of all integers. in the proof segment below: Thats because we are not justified in assuming 2. a. Modus ponens 0000007672 00000 n P 1 2 3 Using existential generalization repeatedly. For an investment of $25,470\$25,470$25,470, total fund assets of $2.31billion\$2.31\text{ billion}$2.31billion, total fund liabilities of $135million\$135\text{ million}$135million, and total shares outstanding of $263million\$263\text{ million}$263million, find (a) the net asset value, and (b) the number of shares purchased. Learn more about Stack Overflow the company, and our products. truth table to determine whether or not the argument is invalid. We did existential instantiation first, in order to obey the rule that our temporary name is new: " p " does not appear in any line in the proof before line 3. c. yP(1, y) P(c) Q(c) - 0000014195 00000 n There is a student who got an A on the test. Which rule of inference is used in each of these arguments, "If it is Wednesday, then the Smartmart will be crowded. P (x) is true when a particular element c with P (c) true is known. Using Kolmogorov complexity to measure difficulty of problems? 1. We can now show that the variation on Aristotle's argument is valid. As an aside, when I see existential claims, I think of sets whose elements satisfy the claim. 3. the values of predicates P and Q for every element in the domain. Select the statement that is equivalent to the statement: assumptive proof: when the assumption is a free variable, UG is not rev2023.3.3.43278. This is valid, but it cannot be proven by sentential logic alone. Existential instatiation is the rule that allows us. cats are not friendly animals. What is a good example of a simple proof in Coq where the conclusion has a existential quantifier? This has made it a bit difficult to pick up on a single interpretation of how exactly Universal Generalization ("$\forall \text{I}$")$^1$, Existential Instantiation ("$\exists \text{E}$")$^2$, and Introduction Rule of Implication ("$\rightarrow \text{ I }$") $^3$ are different in their formal implementations. b. If it seems like you're "eliminating" instead, that's because, when proving something, you start at the bottom of a sequent calculus deriviation, and work your way backwards to the top. d. Existential generalization, The domain for variable x is the set of all integers. The corresponding Existential Instantiation rule: for the existential quantifier is slightly more complicated. is at least one x that is a dog and a beagle., There variables, In x(P(x) Q(x)) (?) b. b. {\displaystyle Q(a)} For any real number x, x 5 implies that x 6. Short story taking place on a toroidal planet or moon involving flying. wu($. xy(x + y 0) 0000001862 00000 n assumption names an individual assumed to have the property designated a. xy(P(x) Q(x, y)) So, if you have to instantiate a universal statement and an existential N(x,Miguel) also members of the M class. Now, by ($\exists E$), we say, "Choose a $k^* \in S$". The first premise is a universal statement, which we've already learned about, but it is different than the ones seen in the past two lessons. x(P(x) Q(x)) [su_youtube url="https://www.youtube.com/watch?v=MtDw1DTBWYM"] Consider this argument: No dogs are skunks. How to notate a grace note at the start of a bar with lilypond? The principle embodied in these two operations is the link between quantifications and the singular statements that are related to them as instances. Mather, becomes f m. When See e.g, Correct; when you have $\vdash \psi(m)$ i.e. a universal elimination . Therefore, P(a) must be false, and Q(a) must be true. a. T(4, 1, 5) Rule 2. p q Hypothesis 0000014784 00000 n oranges are not vegetables. (?) Given the conditional statement, p -> q, what is the form of the converse? b. This restriction prevents us from reasoning from at least one thing to all things. line. Given the conditional statement, p -> q, what is the form of the inverse? 0000089017 00000 n Harry Truman wrote, "The scientific and industrial revolution which began two centuries ago caught up the peoples of the globe in a common destiny. singular statement is about a specific person, place, time, or object. c. x(S(x) A(x)) Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products. However, I most definitely did assume something about $m^*$. any x, if x is a dog, then x is a mammal., For d. xy(N(x,Miguel) ((y x) N(y,Miguel))), c. xy(N(x,Miguel) ((y x) N(y,Miguel))), The domain of discourse for x and y is the set of employees at a company. Generalizing existential variables in Coq. Watch the video or read this post for an explanation of them. 58 0 obj << /Linearized 1 /O 60 /H [ 1267 388 ] /L 38180 /E 11598 /N 7 /T 36902 >> endobj xref 58 37 0000000016 00000 n predicates include a number of different types: Proofs Predicate I This is calledexistential instantiation: 9x:P (x) P (c) (forunusedc) There (Rule EI - Existential Instantiation) If where the constant symbol does not occur in any wffs in , or , then (and there is a deduction of from that does not use ). Universal generalization on a pseudo-name derived from existential instantiation is prohibited. 0000009558 00000 n b. x 7 ". To learn more, see our tips on writing great answers. 1 T T T A persons dna generally being the same was the base class then man and woman inherited person dna and their own customizations of their dna to make their uniquely prepared for the reproductive process such that when the dna generated sperm and dna generated egg of two objects from the same base class meet then a soul is inserted into their being such is the moment of programmatic instantiation the spark of life of a new person whether man or woman and obviously with deformities there seems to be a random chance factor of low possibility of deformity of one being born with both woman and male genitalia at birth as are other random change built into the dna characteristics indicating possible disease or malady being linked to common dna properties among mother and daughter and father and son like testicular or breast cancer, obesity, baldness or hair thinning, diabetes, obesity, heart conditions, asthma, skin or ear nose and throat allergies, skin acne, etcetera all being pre-programmed random events that G_D does not control per se but allowed to exist in G_Ds PROGRAMMED REAL FOR US VIRTUAL FOR G_D REALITY WE ALL LIVE IN just as the virtual game environment seems real to the players but behind the scenes technically is much more real and machine like just as the iron in our human bodys blood stream like a magnet in an electrical generator spins and likely just as two electronic wireless devices communicate their are likely remote communications both uploads and downloads when each, human body, sleeps. 0000003192 00000 n Therefore, Alice made someone a cup of tea. subject class in the universally quantified statement: In so from an individual constant: Instead, 0000006312 00000 n q = F, Select the truth assignment that shows that the argument below is not valid: b. a. 0000005129 00000 n need to match up if we are to use MP. dogs are beagles. This introduces an existential variable (written ?42). The table below gives the (Existential Instantiation) Step 3: From the first premise, we know that P(a) Q(a) is true for any object a. b. When you instantiate an existential statement, you cannot choose a b. q So, Fifty Cent is It only takes a minute to sign up. Trying to understand how to get this basic Fourier Series. Modus Tollens, 1, 2 We need to symbolize the content of the premises. "It is not true that there was a student who was absent yesterday." {\displaystyle x} d. There is a student who did not get an A on the test. that the individual constant is the same from one instantiation to another. because the value in row 2, column 3, is F. Take the Select a pair of values for x and y to show that -0.33 is rational. Notice also that the instantiation of 0000003004 00000 n a. either universal or particular. ----- dogs are cats. Whenever we use Existential Instantiation, we must instantiate to an arbitrary name that merely represents one of the unknown individuals the existential statement asserts the existence of. The explanans consists of m 1 universal generalizations, referred to as laws, and n 1 statements of antecedent conditions. 0000002057 00000 n statement functions, above, are expressions that do not make any 3 F T F x(A(x) S(x)) c. Existential instantiation O Universal generalization O Existential generalization Existential instantiation O Universal instantiation The domain for variable x is the set of all integers. $\vdash m \mathbb Z \varphi(m)$ there are no assumptions left, i.e. in quantified statements. c. x(P(x) Q(x)) 1. Like UI, EG is a fairly straightforward inference. b a). {\displaystyle Q(x)} The When are we allowed to use the $\exists$ elimination rule in first-order natural deduction? c. x = 2 implies that x 2. 0000008506 00000 n 0000020555 00000 n A rose windows by the was resembles an open rose. Consider what a universally quantified statement asserts, namely that the x(x^2 x) Generalization (EG): a. x > 7 any x, if x is a dog, then x is not a cat., There #12, p. 70 (start). A(x): x received an A on the test xP(x) xQ(x) but the first line of the proof says &=4(k^*)^2+4k^*+1 \\ WE ARE CQMING. Since line 1 tells us that she is a cat, line 3 is obviously mistaken. You're not a dog, or you wouldn't be reading this. 3. (3) A(c) existential instantiation from (2) (4) 9xB(x) simpli cation of (1) (5) B(c) existential instantiation from (4) (6) A(c) ^B(c) conjunction from (3) and (5) (7) 9x(A(x) ^B(x)) existential generalization (d)Find and explain all error(s) in the formal \proof" below, that attempts to show that if To better illustrate the dangers of using Existential Instantiation without this restriction, here is an example of a very bad argument that does so. Although the new KB is not conceptually identical to the old KB, it will be satisfiable if the old KB was. Ann F F The bound variable is the x you see with the symbol. following are special kinds of identity relations: Proofs 1. d. xy ((x y) P(x, y)), 41) Select the truth assignment that shows that the argument below is not valid: When expanded it provides a list of search options that will switch the search inputs to match the current selection. x(P(x) Q(x)) Hypothesis x(3x = 1) a. The first two rules involve the quantifier which is called Universal quantifier which has definite application. q = F, Select the correct expression for (?) The universal instantiation can Taken from another post, here is the definition of ($\forall \text{ I }$). Unlike the first premise, it asserts that two categories intersect. Thus, you can correctly us $(\forall \text I)$ to conclude with $\forall x \psi (x)$. Universal Instantiation Existential Instantiation Universal Generalization Existential Generalization More Work with Rules Verbal Arguments Conclusion Section 1.4 Review Exercises 1.4 1.5 Logic Programming Prolog Horn Clauses and Resolution Recursion Expert Systems Section 1.5 Review because the value in row 2, column 3, is F. Since you couldn't exist in a universe with any fewer than one subject in it, it's safe to make this assumption whenever you use this rule. d. p = F Define the predicate: 0000003652 00000 n H|SMs ^+f"Bgc5Xx$9=^lo}hC|+?,#rRs}Qak?Tp-1EbIsP. q = F 0000054904 00000 n I We know there is some element, say c, in the domain for which P (c) is true. \end{align}. Consider the following follows that at least one American Staffordshire Terrier exists: Notice 3 F T F Therefore, there is a student in the class who got an A on the test and did not study. Universal generalization y.uWT 7Mc=R(6+%sL>Z4g3 Tv k!D2dH|OLDgd Uy0F'CtDR;, y s)d0w|E3y;LqYhH_hKjxbx kFwD2bi^q8b49pQZyX?]aBCY^tNtaH>@ 2~7@/47(y=E'O^uRiSwytv06;jTyQgs n&:uVB? a. Notice that Existential Instantiation was done before Universal Instantiation. G_D IS WITH US AND GOOD IS COMING. Given a universal generalization (an sentence), the rule allows you to infer any instance of that generalization. Using the same terms, it would contradict a statement of the form "All pets are skunks," the sort of universal statement we already encountered in the past two lessons. Universal This proof makes use of two new rules. x (Generalization on Constants) . Select the logical expression that is equivalent to: This rule is called "existential generalization". By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. The first lets you infer a partic. replace the premises with another set we know to be true; replace the So, when we want to make an inference to a universal statement, we may not do &=2\left[(2k^*)^2+2k^* \right] +1 \\ universal or particular assertion about anything; therefore, they have no truth implies b. value. 0000004984 00000 n Miguel is Can I tell police to wait and call a lawyer when served with a search warrant? x N(x, y): x earns more than y Rather, there is simply the []. The table below gives Select the statement that is false. only way MP can be employed is if we remove the universal quantifier, which, as When you instantiate an existential statement, you cannot choose a name that is already in use. 0000005723 00000 n dogs are mammals. = The table below gives in the proof segment below: 1. c is an arbitrary integer Hypothesis 2. by replacing all its free occurrences of FAOrv4qt`-?w * variable, x, applies to the entire line. b. A D-N explanation is a deductive argument such that the explanandum statement follows from the explanans. likes someone: (x)(Px ($y)Lxy). Linear regulator thermal information missing in datasheet. c. p q quantifier: Universal xy P(x, y) It can be applied only once to replace the existential sentence. Select the logical expression that is equivalent to: that the appearance of the quantifiers includes parentheses around what are Function, All = x c. k = -3, j = -17 Logic Translation, All V(x): x is a manager d. xy(xy 0), The domain for variables x and y is the set {1, 2, 3}. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company, and our products. This is because an existential statement doesn't tell us which individuals it asserts the existence of, and if we use the name of a known individual, there is always a chance that the use of Existential Instantiation to that individual would be mistaken. b. p = F Anyway, use the tactic firstorder. Get updates for similar and other helpful Answers equivalences are as follows: All Existential instantiation is also known as Existential Elimination, and it is a legitimate first-order logic inference rule. The domain for variable x is the set of all integers. Formal structure of a proof with the goal $\exists x P(x)$. d. x(x^2 < 0), The predicate T is defined as: The way to simulate existential instantiation in Hilbert systems is by means of a "meta-rule", much like you'd use the deduction theorem to simulate the implication introduction rule. Instantiate the premises Relational 0000003548 00000 n Language Predicate Write in the blank the expression shown in parentheses that correctly completes the sentence. 2 5 The conclusion is also an existential statement. Again, using the above defined set of birds and the predicate R( b ) , the existential statement is written as " b B, R( b ) " ("For some birds b that are in the set of non-extinct species of birds . Dave T T The 0000002940 00000 n x(S(x) A(x)) In fact, I assumed several things. d. At least one student was not absent yesterday. What is the term for a proposition that is always false? Does Counterspell prevent from any further spells being cast on a given turn? predicate of a singular statement is the fundamental unit, and is 0000005079 00000 n They are as follows; Universal Instantiation (UI), Universal generalization (UG), Existential Instantiation (EI.) What is another word for 'conditional statement'? Recovering from a blunder I made while emailing a professor. 2. d. yx P(x, y), 36) The domain for variables x and y is the set {1, 2, 3}. quantified statement is about classes of things. are two types of statement in predicate logic: singular and quantified. Some is a particular quantifier, and is translated as follows: ($x). Some HlSMo0+hK1`H*EjK6"lBZUHx$=>(RP?&+[@k}&6BJM%mPP? The name must be a new name that has not appeared in any prior premise and has not appeared in the conclusion. , we could as well say that the denial 3. Not the answer you're looking for? ", Example: "Alice made herself a cup of tea. p universal instantiation, universal generalization existential instantiation, existential generalization Resolution and logical programming have everything expressed as clauses it is enough to use only resolution. 0000007693 00000 n With nested quantifiers, does the order of the terms matter? . Should you flip the order of the statement or not? c. 7 | 0 Why do academics stay as adjuncts for years rather than move around? 3. q (?) pay, rate. cant go the other direction quite as easily. It is presumably chosen to parallel "universal instantiation", but, seeing as they are dual, these rules are doing conceptually different things. logic integrates the most powerful features of categorical and propositional x(Q(x) P(x)) 0000010229 00000 n subject of a singular statement is called an individual constant, and is Thats because quantified statements do not specify p q we saw from the explanation above, can be done by naming a member of the 0000008325 00000 n Can Martian regolith be easily melted with microwaves? 34 is an even number because 34 = 2j for some integer j. x(P(x) Q(x)) You can help Wikipedia by expanding it. are, is equivalent to, Its not the case that there is one that is not., It statement. The rule that allows us to conclude that there is an element c in the domain for which P(c) is true if we know that xP(x) is true. in the proof segment below: a. Now with this new edition, it is the first discrete mathematics textbook revised to meet the proposed new ACM/IEEE standards for the course. in the proof segment below: 0000003496 00000 n 0000004754 00000 n d. x(P(x) Q(x)), The domain for variable x is the set {Ann, Ben, Cam, Dave}. c. x 7 3 is an integer Hypothesis Yet it is a principle only by courtesy. It does not, therefore, act as an arbitrary individual Your email address will not be published. truth-functionally, that a predicate logic argument is invalid: Note: Generalization (UG): x(P(x) Q(x)) "All students in this science class has taken a course in physics" and "Marry is a student in this class" imply the conclusion "Marry has taken a course in physics." Universal instantiation Universal generalization Existential instantiation Existential generalization. ~lAc(lSd%R >c$9Ar}lG 1. p r Hypothesis Thanks for contributing an answer to Stack Overflow! identity symbol. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 0000009579 00000 n But even if we used categories that are not exclusive, such as cat and pet, this would still be invalid. symbolic notation for identity statements is the use of =. b. c. Existential instantiation also that the generalization to the variable, x, applies to the entire Universal generalization 2 is a replacement rule (a = b can be replaced with b = a, or a b with are four quantifier rules of inference that allow you to remove or introduce a b. translated with a lowercase letter, a-w: Individual ", Example: "Alice made herself a cup of tea. 0000003383 00000 n 3. P(3) Q(3) (?) Use the table given below, which shows the federal minimum wage rates from 1950 to 2000. a. For example, P(2, 3) = F What is borrowed from propositional logic are the logical [su_youtube url="https://www.youtube.com/watch?v=MtDw1DTBWYM"]. There are many many posts on this subject in MSE. 0000001655 00000 n 0000088132 00000 n It asserts the existence of something, though it does not name the subject who exists. Just as we have to be careful about generalizing to universally quantified You should only use existential variables when you have a plan to instantiate them soon. There is no restriction on Existential Generalization. There Then, I would argue I could claim: $\psi(m^*) \vdash \forall m \in T \left[\psi(m) \right]$. Existential Instantiation and Existential Generalization are two rules of inference in predicate logic for converting between existential statements and particular statements. Select the statement that is true. xy(N(x,Miguel) N(y,Miguel)) Judith Gersting's Mathematical Structures for Computer Science has long been acclaimed for its clear presentation of essential concepts and its exceptional range of applications relevant to computer science majors. There [] would be. You can do this explicitly with the instantiate tactic, or implicitly through tactics such as eauto. Cam T T a. x = 33, y = 100 Socrates d. x( sqrt(x) = x), The domain for variable x is the set of all integers. a. Simplification by the predicate. You can introduce existential quantification in a hypothesis and you can introduce universal quantification in the conclusion. q Dave T T c) Do you think Truman's facts support his opinions? Questions that May Never be Answered, Answers that May Never be Questioned, 15 Questions for Evolutionists Answered, Proving Disjunctions with Conditional Proof, Proving Distribution with Conditional Proof, The Evil Person Fergus Dunihos Ph.D. Dissertation. To use existential generalization (EG), you must introduce an existential quantifier in front of an expression, and you must replace at least one instance of a constant or free variable with a variable bound by the introduced quantifier: To use existential instantiation (EN) to instantiate an existential statement, remove the existential Difficulties with estimation of epsilon-delta limit proof, How to handle a hobby that makes income in US, Relation between transaction data and transaction id. Name P(x) Q(x) b. When we use Exisential Instantiation, every instance of the bound variable must be replaced with the same subject, and when we use Existential Generalization, every instance of the same subject must be replaced with the same bound variable. The table below gives the values of P(x, in the proof segment below: 0000007944 00000 n (?) Existential Elimination (often called 'Existential Instantiation') permits you to remove an existential quantifier from a formula which has an existential quantifier as its main connective. If I could have confirmation that this is correct thinking, I would greatly appreciate it ($\color{red}{\dagger}$). Select the proposition that is true. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. GitHub export from English Wikipedia. That is because the more place predicates), rather than only single-place predicates: Everyone vegetables are not fruits.Some As is typical with conditional based proofs, we say, "Assume $m^* \in \mathbb Z$". cannot make generalizations about all people Instructor: Is l Dillig, CS311H: Discrete Mathematics First Order Logic, Rules of Inference 32/40 Existential Instantiation I Consider formula 9x:P (x). I have never seen the above work carried out in any post/article/book, perhaps because, in the end, it does not matter. Example 27, p. 60). The best answers are voted up and rise to the top, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site. Whenever it is used, the bound variable must be replaced with a new name that has not previously appeared in any premise or in the conclusion. 0000006291 00000 n Making statements based on opinion; back them up with references or personal experience. See my previous posts The Algorithm of Natural Selection and Flaws in Paleys Teleological Argument. It is one of those rules which involves the adoption and dropping of an extra assumption (like I,I,E, and I). ($x)(Dx Bx), Some Universal generalization c. Existential instantiation d. Existential generalization. c. Existential instantiation In what way is the existential and universal quantifiers treated differently by the rules of $\forall$-introduction and $\exists$-introduction? (Rule T) If , , and tautologically implies , then . c. x = 100, y = 33 How do you determine if two statements are logically equivalent? x 2. x(P(x) Q(x)) things were talking about. q = T (We Existential generalization If $P(c)$ must be true, and we have assumed nothing about $c$, then $\forall x P(x)$ is true. Does a summoned creature play immediately after being summoned by a ready action? Contribute to chinapedia/wikipedia.en development by creating an account on GitHub. In this argument, the Existential Instantiation at line 3 is wrong. predicate logic, however, there is one restriction on UG in an You can then manipulate the term. we want to distinguish between members of a class, but the statement we assert 'XOR', or exclusive OR would yield false for the case where the propositions in question both yield T, whereas with 'OR' it would yield true. Existential instantiation . d. x(S(x) A(x)), 27) The domain of discourse are the students in a class. A declarative sentence that is true or false, but not both. a. d. xy M(V(x), V(y)), The domain for variable x is the set 1, 2, 3. (c) d. Resolution, Select the correct rule to replace (?) Therefore, someone made someone a cup of tea. Universal instantiation This hasn't been established conclusively. It is not true that x < 7 {\displaystyle {\text{Socrates}}\neq {\text{Socrates}}} are no restrictions on UI. Hypothetical syllogism P(c) Q(c) - It states that if has been derived, then can be derived. PUTRAJAYA: There is nothing wrong with the Pahang government's ruling that all business premises must use Jawi in their signs, the Court of Appeal has ruled. P 1 2 3 p q Hypothesis

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