Answer to Question #252156 in Discrete Mathematics for Alice

Question

Make a Fully truth table and identify if it is a tautology, contradiction, contingency.

¬(¬(P∧Q)↔(¬P)∨(¬Q))

Answer 1

$\neg(\neg(P\wedge Q)\longleftrightarrow(\neg P)\vee(\neg Q)\\ \def\arraystretch{1.5} \begin{array}{c|c|c|c|c|c|c|c} P & Q &\neg P&\neg Q& P\wedge Q& \neg(P \wedge Q)&\neg(\neg(P \wedge Q))& \neg P \vee \neg Q \\ \hline T & T &F&F &T&F&T&F\\ T & F &F&T& F&T&F&T\\ F&T&T&F&F&T&F&T\\ F&F&T&T&F&T&F&T \end{array}$

Since the second to the last column is not the same as the last column, then this is a contradiction.