CSC165H1 Study Guide - Midterm Guide: Irrational Number, Contraposition, Rational Number
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CSC165H1 Full Course Notes
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An interpretation for a logical statement consists of a domain d (any non-empty set of elements) and a meaning for each predicate symbol. For example, d = {1, 2} and p (x): x > 0 is an interpretation for the statement x d, p (x) (in this case, one that happens to make the statement true). For each statement below, provide one interpretation under which the statement is true and another interpretation under which the statement is false if either case is not possible, explain why clearly and concisely. X d, y d, p (x, y) True: d = {1}, p (x, y) = true. False: d = {1}, p (x, y) = false. [ x d, [p (x) [ y d, q(x, y)]]] [ x d, p (x)] [ x d, p (x)] True: d = {1, 2}, p (1) = true, p (2) = false, q(1, 1) = q(1, 2) = q(2, 1) = q(2, 2) = true.
