MAT 1348 Lecture Notes - Lecture 2: Logic Puzzle, Logical Biconditional, Contraposition
17 Jan 2017
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Lecture 2: more propositional logic, consistency of a set of propositions, knights and knaves problem. Precedence of logical operators: (cid:1512) conjunction, (cid:1513) disjunction, implication, biconditional. Given an implication p q, we can define (cid:885) other implications: the converse: Q p the contrapositive the inverse. Given: propositional variables x, y, z compound propositions p, q, r. A set {p, q, r, } of compound propositions in the variables x, y, z, is said to be consistentif there exists a truth assignment for x, y, z, that makes propositions. Is the set {s v, v f, f s} consistent? the rows correspond to all possible truth assignments for the proposition. There are (cid:886) rows with all ts, so the set {s v, v f, f s} is continuous. Knights and knaves is a logic puzzle in which 2 there exist two types of people: Say you encounter two individuals, a and b.
