COMP 2711 Ex 1

1

$p$	$q$	$\neg p$	$p\vee q$	$\neg ((p\vee q)\wedge \neg p)$	$\neg ((p\vee q)\wedge \neg p)\wedge \neg p$
T	T	F	T	T	F
T	F	F	T	T	F
F	T	T	T	F	F
F	F	T	F	T	T

2

$$\begin{array}{rl}& (\neg p\wedge (\neg p\wedge q))\vee (p\wedge (p\wedge \neg q))\\ & \equiv ((\neg p\wedge \neg p)\wedge q)\vee ((p\wedge p)\wedge \neg q)\\ & \equiv (\neg p\wedge q)\vee (p\wedge \neg q)\end{array}$$

The statements are logically equivalent