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135_1_-_Solutions

135_1_-_Solutions - Assignment 1 Solutions 1 Is the...

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Assignment 1 – Solutions 1. Is the statement P = ( Q = R ) equivalent to ( P = Q ) = R ? Give reasons. Solution 1: The statements are not equivalent. To see this let P , Q and R be all false. Then ( Q = R ) and ( P = Q ) are true. Therefore P = ( Q = R ) is true but ( P = Q ) = R is false. Solution 2: P Q R Q = R P = ( Q = R ) T T T T T T T F F F T F T T T T F F T T F T T T T F T F F T F F T T T F F F T T P Q R P = Q ( P = Q ) = R T T T T T T T F T F T F T F T T F F F T F T T T T F T F T F F F T T T F F F T F Since the final columns are not the same, the two statements are not equivalent. In particular, they differ in the bottom row, so the truth value of the statements are different when P , Q and R are all false. 2. Prove that the statements P OR ( Q AND R ) and ( P OR Q ) AND ( P OR R ) have the same truth tables. This is a distributive law . Solution: P Q R Q AND R P OR ( Q AND R ) T T T T T T T F F T T F T F T T F F F T F T T T T F T F F F F F T F F F F F F F 1
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P Q R P OR Q P OR R ( P OR Q ) AND ( P OR R ) T T T T T T T T F
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