A Truth Table For A Conjunction Its Negation

We know that $P\wedge Q$ is false unless both $P$ and $Q$ are both true. There are four cases to consider when looking at the truth values of $P$ and $Q$, hence our truth table has 4 rows. This gives us the third column in the truth table below for $P\wedge Q$. The fourth column below contains the truth values for $\sim(P\wedge Q)$ by just interchanging the $T$ and $F$ values from the third column. $$ \begin{array}{c|c|c} P&Q&P\wedge Q&\sim(P\wedge Q) \\\hline T&T&T&F\\ T&F&F&T\\ F&T&F&T\\ F&F&F&T \end{array} $$