Question

The boolean expression $(\sim (p\wedge q))\vee q$ is equivalent to:

• A. $p\to q$
• B. $p\to (p\to q)$
• C. $q\to (p\wedge q)$
• D. $p\to (p\vee q)$

Answer 1

The correct option is D $p\to (p\vee q)$

Making truth table
$\begin{array}{cccccccc}p& q& p\wedge q& \sim (p\wedge q)& (\sim (p\wedge q\left)\right)\vee q& p\vee q& p\to q& p\to (p\vee q)\\ T& T& T& F& T& T& T& T\\ T& F& F& T& T& T& F& T\\ F& T& F& T& T& T& T& T\\ F& F& F& T& T& F& T& T\\ & & & & \text{Tautology}& & & \text{Tautology}\end{array}$

$\therefore (\sim (p\wedge q\left)\right)\vee q\equiv p\to (p\vee q)$