Question

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

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

Answer 1

Answer: (B)

p	q	$q\to p$	$p\to \left(q\to p\right)$	$p\vee q$	$p\to \left(p\vee q\right)$
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 $p\to \left(q\to p\right)$ and $p\to \left(p\vee q\right)$ are same, hence $p\to \left(q\to p\right)$ is equivalent to $p\to \left(p\vee q\right).$