L23_Predicates_andS_Syllogisms

L23_Predicates_andS_Syllogisms - Predicates and Syllogisms...

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Predicates and Syllogisms Informally, a statement with a variable in it is called a “predicate” . Example: “x is a dog” or “t is greater than 3” . Technically, these are not statements since we have not said what x or t is, so we use a different word and refer to these as “predicates” instead of “statements” . More precisely, to talk about predicates we start with a set U called the “universe”; a predicate for U must become a statement whenever the variable is replaced by an element of U. Example: Let U denote the set of all students and watches at LSU and let p(x) be the predicate: “x is a person.” Then p(Tom) is the statement “Tom is a person”, which is a true statement, and p(Jim’s watch) is the statement “Jim’s watch is a person”, which is false.
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By definition, a predicate p(x) is true provided that every one of the statements p(u) obtained by replacing x by u in U is true. Example: Let U = {2,4,6} and let p(x): x>1. Then p(x) is true since p(2), p(4), and p(6) are true.
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Given two predicates p(x), q(x), and a universe U, the implication p(x) 0 q(x) is true provided that whenever x is replaced by an element of U the resulting implication of statements is true. Summary: For predicates, “true” means “always true”. An implication of predicates p(x) 0 q(x) is false if there is at least one element u of U for which the implication p(u) 0 q(u) is false. Summary:
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This note was uploaded on 10/11/2011 for the course PSYC, PSYC 2076, 2060 taught by Professor Briganti,gustan,perlis,namikas,wheeler during the Spring '10 term at LSU.

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L23_Predicates_andS_Syllogisms - Predicates and Syllogisms...

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