## Thinking Mathematically (6th Edition)

$\begin{array}{llll} p & q & \sim q & \sim q\wedge p\\ \hline T & T & F & F\\ T & F & T & T\\ F & T & F & F\\ F & F & T & F \end{array}$
Set up a truth table for two inputs, p and q: $\begin{array}{llll} p & q & ... & ...\\ \hline T & T & & \\ T & F & & \\ F & T & & \\ F & F & & \end{array}$ Fill column for $\sim q$, using the truth table for negation, $\begin{array}{llll} p & q & \sim q & ...\\ \hline T & T & F & \\ T & F & T & \\ F & T & F & \\ F & F & T & \end{array}$ Now, use the conjunction truth table when columns 3 and 1 give inputs (true only when both are true) $\begin{array}{llll} p & q & \sim q & \sim q\wedge p\\ \hline T & T & F & F\\ T & F & T & T\\ F & T & F & F\\ F & F & T & F \end{array}$