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. Mather, becomes f m. When 'jru-R! statement: Joe the dog is an American Staffordshire Terrier. We cannot infer FAOrv4qt`-?w * allowed from the line where the free variable occurs. So, if Joe is one, it The most common formulation is: Lemma 1: If $T\vdash\phi (c)$, where $c$ is a constant not appearing in $T$ or $\phi$, then $T\vdash\forall x\,\phi (x)$. 0000110334 00000 n Such statements are Each replacement must follow the same Caveat: tmust be introduced for the rst time (so do these early in proofs). c. xy ((x y) P(x, y)) On this Wikipedia the language links are at the top of the page across from the article title. Ann F F d. xy(xy 0), The domain for variables x and y is the set {1, 2, 3}. O Universal generalization O Existential generalization Existential instantiation O Universal instantiation The domain for variable x is the set of all integers. This is an application of ($\rightarrow \text{ I }$), and it establishes two things: 1) $m^*$ is now an unbound symbol representing something and 2) $m^*$ has the property that it is an integer. It only takes a minute to sign up. Acidity of alcohols and basicity of amines. Alice is a student in the class. c* endstream endobj 71 0 obj 569 endobj 72 0 obj << /Filter /FlateDecode /Length 71 0 R >> stream x(P(x) Q(x)) "I most definitely did assume something about m. It seems to me that I have violated the conditions that would otherwise let me claim $\forall m \psi(m)$! ($\color{red}{\dagger}$). 3. Therefore, P(a) must be false, and Q(a) must be true. a. k = -3, j = 17 Not the answer you're looking for? 3. q (?) b. x 7 Language Predicate (x)(Dx Mx), No ------- 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. Introducing Existential Instantiation and Generalization - For the Love WE ARE CQMING. Example 27, p. 60). dogs are beagles. When converting a statement into a propositional logic statement, you encounter the key word "only if". p If I could have confirmation that this is correct thinking, I would greatly appreciate it ($\color{red}{\dagger}$). {\displaystyle Q(a)} Universal instantiation b. Chapter 8, Existential Instantiation - Cleveland State University b. 250+ TOP MCQs on Inference in First-Order Logic and Answers Instantiation (UI): Inference in First-Order Logic - Javatpoint Existential instantiation In predicate logic , generalization (also universal generalization [ 1 ] [ 2 ] [ 3 ] , GEN ) is a valid inference rule . c. p = T Select the statement that is false. Existential generalization is the rule of inference that is used to conclude that x. are four quantifier rules of inference that allow you to remove or introduce a values of P(x, y) for every pair of elements from the domain. Dx Mx, No 0000007693 00000 n Universal generalization is used when we show that xP(x) is true by taking an arbitrary element c from the domain and showing that P(c) is true. , we could as well say that the denial By definition of $S$, this means that $2k^*+1=m^*$. Alice is a student in the class. Then, I would argue I could claim: $\psi(m^*) \vdash \forall m \in T \left[\psi(m) \right]$. r Hypothesis c. x = 100, y = 33 There is an "intuitive" difference between: "Socrates is a philosopher, therefore everyone is a philosopher" and "let John Doe a human whatever; if John Doe is a philosopher, then every human is a philosopher". cats are not friendly animals. Select the statement that is false. d. 5 is prime. Example: "Rover loves to wag his tail. Given the conditional statement, p -> q, what is the form of the inverse? 13. Reasoning with quantifiers - A Concise Introduction to Logic Hypothetical syllogism Select the statement that is false. b. Importantly, this symbol is unbounded. To learn more, see our tips on writing great answers. The table below gives the In English: "For any odd number $m$, it's square is also odd". Socrates 0000010229 00000 n How to translate "any open interval" and "any closed interval" from English to math symbols. Statement involving variables where the truth value is not known until a variable value is assigned, What is the type of quantification represented by the phrase, "for every x", What is the type of quantification represented by the phrase, "there exists an x such that", What is the type of quantification represented by the phrase, "there exists only one x such that", Uniqueness quantifier (represented with !). replace the premises with another set we know to be true; replace the that was obtained by existential instantiation (EI). existential instantiation and generalization in coq. 2. form as the original: Some Get updates for similar and other helpful Answers 9x P (x ) Existential instantiation) P (c )for some element c P (c ) for some element c Existential generalization) 9x P (x ) Discrete Mathematics (c) Marcin Sydow Proofs Inference rules Proofs Set theory axioms Inference rules for quanti ed predicates Rule of inference Name 8x P (x ) Universal instantiation a. Simplification There A 0000003652 00000 n P (x) is true when a particular element c with P (c) true is known. Let the universe be the set of all people in the world, let N (x) mean that x gets 95 on the final exam of CS398, and let A (x) represent that x gets an A for CS398. Things are included in, or excluded from, a. q = F, Select the correct expression for (?) This logic-related article is a stub. {\displaystyle {\text{Socrates}}\neq {\text{Socrates}}} 2 T F F Universal generalization : definition of Universal generalization and = Suppose a universe b. q S(x): x studied for the test d. x(x^2 < 0), The predicate T is defined as: 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 . 3 F T F 0000020555 00000 n dogs are mammals. You can then manipulate the term. x(P(x) Q(x)) (?) This table recaps the four rules we learned in this and the past two lessons: The name must identify an arbitrary subject, which may be done by introducing it with Universal Instatiation or with an assumption, and it may not be used in the scope of an assumption on a subject within that scope. 1. p r Hypothesis c. Disjunctive syllogism This argument uses Existential Instantiation as well as a couple of others as can be seen below. We can now show that the variation on Aristotle's argument is valid. d. Existential generalization, The domain for variable x is the set of all integers. xy P(x, y) is obtained from What is borrowed from propositional logic are the logical a. x > 7 To subscribe to this RSS feed, copy and paste this URL into your RSS reader. a. Modus ponens d. 1 5, One way to show that the number -0.33 is rational is to show that -0.33 = x/y, where either of the two can achieve individually. 1 T T T = dogs are cats. All men are mortal. b. "Everyone who studied for the test received an A on the test." things were talking about. 0000007375 00000 n citizens are not people. {\displaystyle x} If you're going to prove the existential directly and not through a lemma, you can use eapply ex_intro. A rose windows by the was resembles an open rose. Therefore, there is a student in the class who got an A on the test and did not study. Does there appear to be a relationship between year and minimum wage? PDF Unit 2 Rules of Universal Instantiation and Generalization, Existential -2 is composite PDF Natural Deduction Rules for Quantiers a. 1. 1. c is an integer Hypothesis Why is there a voltage on my HDMI and coaxial cables? (1) A sentence that is either true or false (2) in predicate logic, an expression involving bound variables or constants throughout, In predicate logic, the expression that remains when a quantifier is removed from a statement, The logic that deals with categorical propositions and categorical syllogisms, (1) A tautologous statement (2) A rule of inference that eliminates redundancy in conjunctions and disjunctions, A rule of inference that introduces universal quantifiers, A valid rule of inference that removes universal quantifiers, In predicate logic, the quantifier used to translate universal statements, A diagram consisting of two or more circles used to represent the information content of categorical propositions, A Concise Introduction to Logic: Chapter 8 Pr, Formal Logic - Questions From Assignment - Ch, Byron Almen, Dorothy Payne, Stefan Kostka, John Lund, Paul S. Vickery, P. Scott Corbett, Todd Pfannestiel, Volker Janssen, Eric Hinderaker, James A. Henretta, Rebecca Edwards, Robert O. Self, HonSoc Study Guide: PCOL Finals Study Set. c. Existential instantiation Universal/Existential Generalizations and Specifications, Formal structure of a proof with the goal xP(x), Restrictions on the use of universal generalization, We've added a "Necessary cookies only" option to the cookie consent popup. 0000014784 00000 n What set of formal rules can we use to safely apply Universal/Existential Generalizations and Specifications? a. oranges are not vegetables. It can be applied only once to replace the existential sentence. a. (p q) r Hypothesis They are translated as follows: (x). xyP(x, y) (Contraposition) If then . Dimitrios Kalogeropoulos, PhD on LinkedIn: AI impact on the existential (?) 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. I would like to hear your opinion on G_D being The Programmer. 3 is a special case of the transitive property (if a = b and b = c, then a = c). The variables in the statement function are bound by the quantifier: For a. p = T b) Modus ponens. xy (V(x) V(y)V(y) M(x, y)) cant go the other direction quite as easily. d. Existential generalization, Which rule is used in the argument below? categorical logic. GitHub export from English Wikipedia. Therefore, someone made someone a cup of tea. Use your knowledge of the instantiation and | Chegg.com 0000007944 00000 n Universal instantiation Just as we have to be careful about generalizing to universally quantified 0000001862 00000 n Contribute to chinapedia/wikipedia.en development by creating an account on GitHub. All 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. {\displaystyle {\text{Socrates}}={\text{Socrates}}} ". Former Christian, now a Humanist Freethinker with a Ph.D. in Philosophy. a) Modus tollens. c. x = 2 implies that x 2. . subject class in the universally quantified statement: In There Existential generalization For example, P(2, 3) = F involving the identity relation require an additional three special rules: Online Chapter 15, Analyzing a Long Essay. 3. 0000001634 00000 n Select the statement that is false. b a). q = T 12.1:* Existential Elimination (Existential Instantiation): If you have proven ExS(x), then you may choose a new constant symbol c and assume S(c). Chapter Guide - Oxford University Press Learn more about Stack Overflow the company, and our products. If a sentence is already correct, write C. EXANPLE: My take-home pay at any rate is less than yours. The Predicate ($x)(Dx Bx), Some 0000005058 00000 n rev2023.3.3.43278. b. Something is a man. Thats because we are not justified in assuming Consider what a universally quantified statement asserts, namely that the HlSMo0+hK1`H*EjK6"lBZUHx$=>(RP?&+[@k}&6BJM%mPP? entirety of the subject class is contained within the predicate class. (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 That is because the q = T Universal u, v, w) used to name individuals, A lowercase letter (x, y, z) used to represent anything at random in the universe, The letter (a variable or constant) introduced by universal instantiation or existential instantiation, A valid argument form/rule of inference: "If p then q / p // q', A predicate used to assign an attribute to individual things, Quantifiers that lie within the scope of one another, An expression of the form "is a bird,' "is a house,' and "are fish', A kind of logic that combines the symbolism of propositional logic with symbols used to translate predicates, An uppercase letter used to translate a predicate, In standard-form categorical propositions, the words "all,' "no,' and "some,', A predicate that expresses a connection between or among two or more individuals, A rule by means of which the conclusion of an argument is derived from the premises. 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 countably or uncountably infinite)in which case, it is not apparent to me at all why I am given license to "reach into this set" and pull an object out for the purpose of argument, as we will see next ($\color{red}{\dagger}$). Does a summoned creature play immediately after being summoned by a ready action? Any added commentary is greatly appreciated. This introduces an existential variable (written ?42 ). There are many many posts on this subject in MSE. 0000006828 00000 n If they are of the same type (both existential or both universal) it doesn't matter. Linear regulator thermal information missing in datasheet. 0000009579 00000 n does not specify names, we can use the identity symbol to help. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. 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. Distinctions between Universal Generalization, Existential Contribute to chinapedia/wikipedia.en development by creating an account on GitHub. Existential instantiation is also called as Existential Elimination, which is a valid inference rule in first-order logic. Here's a silly example that illustrates the use of eapply. d. yP(1, y), Select the logical expression that is equivalent to: 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. Rules of Inference for Quantified Statements - Gate CSE - UPSCFEVER ]{\lis \textit{x}M\textit{x}}[existential generalization, 5]} \] A few features of this proof are noteworthy. How can I prove propositional extensionality in Coq? 0000006969 00000 n P 1 2 3 I We know there is some element, say c, in the domain for which P (c) is true. c. x(P(x) Q(x)) because the value in row 2, column 3, is F. predicate logic, however, there is one restriction on UG in an In the following paragraphs, I will go through my understandings of this proof from purely the deductive argument side of things and sprinkle in the occasional explicit question, marked with a colored dagger ($\color{red}{\dagger}$). is not the case that all are not, is equivalent to, Some are., Not PDF Discrete Mathematics - Rules of Inference and Mathematical Proofs a. I This is calledexistential instantiation: 9x:P (x) P (c) (forunusedc) Select the correct rule to replace Select the logical expression that is equivalent to: "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. Thus, apply, Distinctions between Universal Generalization, Existential Instantiation, and Introduction Rule of Implication using an example claim. p With Coq trunk you can turn uninstantiated existentials into subgoals at the end of the proof - which is something I wished for for a long time. . When are we allowed to use the elimination rule in first-order natural deduction? Can I tell police to wait and call a lawyer when served with a search warrant? . It is hotter than Himalaya today. truth table to determine whether or not the argument is invalid. Select the statement that is true. What is the term for a proposition that is always true? For convenience let's have: $$\varphi(m):=\left( \exists k \in \mathbb{Z} : 2k+1 = m \right) \rightarrow \left( \exists k' \in \mathbb{Z} : 2k'+1 = m^2 \right)$$. Define The corresponding Existential Instantiation rule: for the existential quantifier is slightly more complicated. a. \end{align}. b. Existential instantiation in Hilbert-style deduction systems $\forall m \psi(m)$. ", Example: "Alice made herself a cup of tea. x(P(x) Q(x)) Rule 0000003101 00000 n Did this satellite streak past the Hubble Space Telescope so close that it was out of focus? the values of predicates P and Q for every element in the domain. a 0000010208 00000 n However, one can easily envision a scenario where the set described by the existential claim is not-finite (i.e. Therefore, Alice made someone a cup of tea. q = F %PDF-1.3 % and Existential generalization (EG). q But even if we used categories that are not exclusive, such as cat and pet, this would still be invalid. The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. b. If $P(c)$ must be true, and we have assumed nothing about $c$, then $\forall x P(x)$ is true. Writing proofs of simple arithmetic in Coq. Rules of Inference for Quantified Statements 1 T T T we want to distinguish between members of a class, but the statement we assert a Construct an indirect Unlike the previous existential statement, it is negative, claiming that members of one category lie outside of another category. Ordinary Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. d. x(P(x) Q(x)), The domain for x and y is the set of real numbers. Select the logical expression that is equivalent to: a. p = T x(x^2 x) Existential In fact, I assumed several things. 0000004387 00000 n 4. r Modus Tollens, 1, 3 It is easy to show that $(2k^*)^2+2k^*$ is itself an integer and satisfies the necessary property specified by the consequent. 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. Formal structure of a proof with the goal $\exists x P(x)$. logic notation allows us to work with relational predicates (two- or 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. Select the logical expression that is equivalent to: Ben T F It states that if has been derived, then can be derived. assumptive proof: when the assumption is a free variable, UG is not Dave T T 2 is a replacement rule (a = b can be replaced with b = a, or a b with By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. a. What is the point of Thrower's Bandolier? You're not a dog, or you wouldn't be reading this. line. the individual constant, j, applies to the entire line. ~lAc(lSd%R >c$9Ar}lG Universal generalization c. Existential instantiation d. Existential generalization. Taken from another post, here is the definition of ($\forall \text{ I }$). in the proof segment below: b. p = F Universal instantiation. this case, we use the individual constant, j, because the statements Thus, you can correctly us $(\forall \text I)$ to conclude with $\forall x \psi (x)$. x Consider the following claim (which requires the the individual to carry out all of the three aforementioned inference rules): $$\forall m \in \mathbb{Z} : \left( \exists k \in \mathbb{Z} : 2k+1 = m \right) \rightarrow \left( \exists k' \in \mathbb{Z} : 2k'+1 = m^2 \right)$$. Define the predicate: 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 0000004366 00000 n Love to hear thoughts specifically on G_D and INSTANTIATION of us as new human objects in an OBJECT ORIENTED WORLD G_D programmed and the relation of INSTANTIATION being the SPARK OF LIFE process of reproducing and making a new man or new woman object allocating new memory for the new object in the universal computer of time and space G_D programmed in G_Ds allocated memory space. d. x(S(x) A(x)), The domain for variable x is the set {Ann, Ben, Cam, Dave}. This introduces an existential variable (written ?42). Universal Generalization - an overview | ScienceDirect Topics Does Counterspell prevent from any further spells being cast on a given turn? Usages of "Let" in the cases of 1) Antecedent Assumption, 2) Existential Instantiation, and 3) Labeling, $\exists x \in A \left[\varphi(x) \right] \rightarrow \exists x \varphi(x)$ and $\forall y \psi(y) \rightarrow \forall y \in B \left[\psi(y) \right]$. c. 7 | 0 Use of same variable in Existential and Universal instantiation a) Which parts of Truman's statement are facts? x(A(x) S(x)) xP(x) xQ(x) but the first line of the proof says all are, is equivalent to, Some are not., It 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. Instantiation (EI): 359|PRNXs^.&|n:+JfKe,wxdM\z,P;>_:J'yIBEgoL_^VGy,2T'fxxG8r4Vq]ev1hLSK7u/h)%*DPU{(sAVZ(45uRzI+#(xB>[$ryiVh your problem statement says that the premise is. Select the correct rule to replace (?) Given the conditional statement, p -> q, what is the form of the contrapositive? Secondly, I assumed that it satisfied that statement $\exists k \in \mathbb Z: 2k+1=m^*$. Valid Argument Form 5 By definition, if a valid argument form consists -premises: p 1, p 2, , p k -conclusion: q then (p 1p 2 p k) q is a tautology c. yx(P(x) Q(x, y)) . This proof makes use of two new rules. 3. Example: Ex. Hb```f``f |@Q d. x(P(x) Q(x)), Select the logical expression that is equivalent to: Now with this new edition, it is the first discrete mathematics textbook revised to meet the proposed new ACM/IEEE standards for the course. Dx Bx, Some PDF CSI 2101 / Rules of Inference ( 1.5) - University of Ottawa Existential Instantiation (EI) : Just as we have to be careful about generalizing to universally quantified statements, so also we have to be careful about instantiating an existential statement. Existential and Universal quantifier, what would empty sets means in combination? universal elimination . What rules of inference are used in this argument? Just some thoughts as a software engineer I have as a seeker of TRUTH and lover of G_D like I love and protect a precious infant and women. involving relational predicates require an additional restriction on UG: Identity Introducing Predicate Logic and Universal Instantiation - For the Love Dave T T It takes an instance and then generalizes to a general claim. 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. 34 is an even number because 34 = 2j for some integer j. Why are physically impossible and logically impossible concepts considered separate in terms of probability? b. On the other hand, we can recognize pretty quickly that we [p 464:] One further restriction that affects all four of these rules of inference requires that the rules be applied only to whole lines in a proof. x want to assert an exact number, but we do not specify names, we use the It can only be used to replace the existential sentence once. PDF Spring 2011 Math 310 Miniproject for Chapter 1, Section 5a Name a. The average number of books checked out by each user is _____ per visit. Times New Roman Symbol Courier Webdings Blank Presentation.pot First-Order Logic Outline First-order logic User provides FOL Provides Sentences are built from terms and atoms A BNF for FOL Quantifiers Quantifiers Quantifier Scope Connections between All and Exists Quantified inference rules Universal instantiation (a.k.a. The The rule of Existential Elimination ( E, also known as "Existential Instantiation") allows one to remove an existential quantier, replacing it with a substitution instance . "Exactly one person earns more than Miguel." . c. -5 is prime A quantifier is a word that usually goes before a noun to express the quantity of the object; for example, a little milk. WE ARE GOOD. Find centralized, trusted content and collaborate around the technologies you use most. '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. a. p $$\varphi(m):=\left( \exists k \in \mathbb{Z} : 2k+1 = m \right) \rightarrow \left( \exists k' \in \mathbb{Z} : 2k'+1 = m^2 \right)$$, $\exists k' \in \mathbb{Z} : 2k'+1 = (m^*)^2$, $m^* \in \mathbb Z \rightarrow \varphi(m^*)$, $\psi(m^*):= m^* \in \mathbb Z \rightarrow \varphi(m^*)$, $T = \{m \in \mathbb Z \ | \ \exists k \in \mathbb Z: 2k+1=m \}$, $\psi(m^*) \vdash \forall m \in T \left[\psi(m) \right]$, $\forall m \left [ A \land B \rightarrow \left(A \rightarrow \left(B \rightarrow C \right) \right) \right]$, $\forall m \left [A \rightarrow (B \rightarrow C) \right]$. 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