Below you will find multiple truth tables. Finish filling out the truth tables and then use them to determine if the coresponding propositions are equivalent.

                 
P Q P ∧\displaystyle \wedge Q ~(P ∧\displaystyle \wedge Q)
T T
T F
F T
F F
                 
P Q Q ∨\displaystyle \vee P ~(Q ∨\displaystyle \vee P)
T T
T F
F T
F F
                 
P Q ~ P ~ Q ~P ∧\displaystyle \wedge ~Q
T T
T F
F T
F F
                 
P Q ~ P ~ Q ~Q ∨\displaystyle \vee ~P
T T
T F
F T
F F


Mark each of the following as either true or false based on the truth tables you have created above.

~(P ∧\displaystyle \wedge Q) ≡\displaystyle \equiv ~(P ∨\displaystyle \vee Q)

~(P ∧\displaystyle \wedge Q) ≡\displaystyle \equiv ~P ∧\displaystyle \wedge ~Q

~(P ∧\displaystyle \wedge Q) ≡\displaystyle \equiv ~P ∨\displaystyle \vee ~Q

~(P ∨\displaystyle \vee Q) ≡\displaystyle \equiv ~(P ∧\displaystyle \wedge Q)

~(P ∨\displaystyle \vee Q) ≡\displaystyle \equiv ~P ∧\displaystyle \wedge ~Q

~(P ∨\displaystyle \vee Q)≡\displaystyle \equiv ~P ∨\displaystyle \vee ~Q

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