s E T" is a tautology. This can be proved (or disproved) using a truth table. 2) RU(SnT) = (RUS)n(RUT). 3 Proofs in Set Theory 45 In writing the table, it is implicitly assumed that a general element x is being considered; the notation T (or F) under the name of a set means that the statement that x is a member of that set is true (or false).

Solution. We proceed in steps as before. The result is p q T T T rvq F pl\rvq F F T T F F T F F T F F qVp (pl\rvq) ----t (qV p) T T T T T T T F Practice Exercise. Find the truth table for (pV rvq) := (q ----t p). 5 is in fact a tautology. A compound statement is a tautology if it is always true, regardless of the truth values of the simple statements from which it is constructed. A statement that is always false is called a contradiction; a very simple example is pi\ rvp. Other statements that do not fall into either category are called contingent.

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A Beginner’s Guide to Discrete Mathematics by W.D. Wallis


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