Question

The statement $p \rightarrow \left(q\,\rightarrow \,p\right) $ is equivalent to:

• A. $p \rightarrow q $
• B. $p \rightarrow \left(p\,\vee\,q\right) $
• C. $p \rightarrow \left(p\,\rightarrow \,q\right) $
• D. $p \rightarrow \left(q\,\wedge \,p\right) $

Answer 1

Answer: (B)

p	q	$q \rightarrow p$	$p \rightarrow\left(q \rightarrow p\right)$	$p\,\vee\,q$	$p \rightarrow \left(p\,\vee \,q\right)$
T	T	T	T	T	T
T	F	F	T	T	T
F	T	T	T	T	T
F	F	T	T	F	T

Since truth value of $p \rightarrow \left(q\,\rightarrow \,p\right)$ and $p \rightarrow \left(p\,\vee\,q\right)$ are same, hence $p \rightarrow \left(q\,\rightarrow \,p\right)$ is equivalent to $p \rightarrow \left(p\,\vee \,q\right).$