Question: Show that the following are logical equivalent using truth tables. a) ((P Q) ^(P R)) = (P (Q ^ R)) b) (P R) V

Show that the following are logical equivalent using truth tables. a) ((P

Show that the following are logical equivalent using truth tables. a) ((P Q) ^(P R)) = (P (Q ^ R)) b) (P R) V (Q R) = (P ^ Q) R c) P Q = Q d) (PQ) = P Q

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To show logical equivalence using truth tables we need to construct truth tables for both expressions and compare the results a Lets start with the truth table for PQPR P QR Q R T T T F TFT TFF P T T F F F F TT TF P T T T F F T F F F F F PQ T T F F T T T T Q R T T T T F F FT T TFF F T TT T F F T F F PR PR T F T F T T T T T T T b Lets create the truth table for PR V QR PQ R PQPR T F F QR T F T T T F T T F T T T T The last column shows that both expressions have the same truth values for all combinations of truth values of P Q and R Thus they are logically equivalent PRVQR T F T T T QR T F F F T F T F F T T PQ T T F F F F F PQR F T F F F T T T T PQR T F T T T T T T Again the last column shows that both expressions have the same truth values for all combinations of truth values of P Q and R Thus they are logically equivalent c The expression ... View full answer

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