SOLUTION: Verify the following if and only if statements using truth tables: 1) ~ (P ^ Q) <=> (~P) V (~Q) 2) ~( P<=>Q) <=> P ^ ~(Q)

Question 934684: Verify the following if and only if statements using truth tables:
1) ~ (P ^ Q) <=> (~P) V (~Q)
2) ~( P<=>Q) <=> P ^ ~(Q)
Answer by ptfile(81) (Show Source): You can put this solution on YOUR website!

p  q ~p ~q (P^Q) (P)V(Q) ~(P^Q) (~P)V(~Q) ~(P^Q)<=>(~P)V(~Q)
T  T  F  F   T      T       F       F            T
T  F  F  T   F      T       T       T            T
F  T  T  F   F      T       T       T            T
F  F  T  T   F      F       T       T            T

p  q ~q (P<=>Q) P^(Q) ~(P<=>Q) P^~(Q) ~(P<=>Q)<=>P^~(Q)
T  T  F    T     T        F     F              T
T  F  T    F     F        T     T              T
F  T  F    F     F        T     F              F
F  F  T    T     F        F     F              T

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