Question

Use a truth table to verify this De Morgan’s law:

¬(p ∧ q) ≡ ¬p ∨ ¬q

Answer 1

Let us use a truth table to verify this De Morgan’s law:

$¬(p ∧ q) ≡ ¬p ∨ ¬q.$

We have the following trush table:

$\begin{array}{||c|c||c|c|c|c|c||} \hline\hline p & q & p\land q & \neg p & \neg q & \neg(p\land q) & \neg p\lor\neg q\\ \hline\hline F & F & F & T & T & T & T \\ \hline F & T & F & T & F & T & T \\ \hline T & F & F & F & T & T & T\\ \hline T & T & T & F & F & F & F \\ \hline\hline \end{array}$

Since the last two columns are coinside, we conclude that the De Morgan’s law is indeed true.