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Unformatted text preview: t is both closed and bounded. It is bounded since diam(X) = b - a < . (b) The set X is not open since a X but B (a) = (a - , a + ). Clearly, a - > a < 0. Therefore, the set X is not open. (d) Since X is closed, the closure of X is simply X. 6. Do all of the following. (b) Construct a truth table for the propositional form [(S P ) (S R)] P . (c) Are the above two propositional forms equivalent? Explain. (a) Construct a truth table for the propositional form [(P R) (R P )] (S S). (d) Are any of the above two propositional forms a tautology or a contradiction? Explain why or why not. Solution: (a) The truth-table is: P T T T T F F F F (b) The truth-table is: P T T T T F F F F R T T F F T T F F S T F T F T F T F [(S P ) (S R)] P T F T T T T T T 7 R T T F F T T F F S T F T F T F T F [(P R) (R P )] (S S) T T F F F F T T (c) Since the truth tables are dierent they are not equivalent. (d) Neither of the propositional forms are tautologies or contradictions as neither of the propositional forms are everywhere true or false. 8...
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This document was uploaded on 03/20/2014 for the course ECON 2p30 at Brock University, Canada.
- Fall '12