Kenneth Rosen Edition 7 Exercise 1.3 Question 27 (Page No. 35)

Question

Show that $p \leftrightarrow q$ and $(p \rightarrow q) \wedge (q \rightarrow p)$ are logically equivalent.

Answer 1

${\color{Red}{p \leftrightarrow q\equiv(p \rightarrow q) \wedge (q \rightarrow p)} }$

Truth table

$p$	$q$	$p\rightarrow q$	$q\rightarrow p$	$(q\rightarrow p)\wedge (q\rightarrow p)$	$p\leftrightarrow q$
T	T	T	T	T	T
T	F	F	T	F	F
F	T	T	F	F	F
F	F	T	T	T	T

Answer 2