Kenneth Rosen Edition 7 Exercise 1.3 Question 49 (Page No. 36)

Question

Show that $p\downarrow q$ is logically equivalent to $\sim(p \vee q).$

Answer 1

.......

Answer 2

${\color{Red}{p\downarrow q\equiv\sim(p \vee q)} }$

we can simply use the truth table

$p$	$q$	$p\vee q$	$\sim(p\vee q)$	$p\downarrow q$
T	T	T	F	F
T	F	T	F	F
F	T	T	F	F
F	F	F	T	T

Answer 3