Question

The statement $p\to (q\to p)$ is equivalent to

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

Answer 1

The correct option is A

$p\to (p\vee q)$

Explanation for correct option:

Given, $p\to (q\to p)$

$$\begin{gathered} p\to (q\to p)=~p\vee (q\to p) \\ =~p\vee (~q\vee p) \end{gathered}$$

since $p\vee ~p$ is always true,

$$\begin{gathered} =~p\vee p\vee q \\ =p\to (p\vee q) \end{gathered}$$

Thus, $p\to (q\to p)$ is equivalent to $p\to (p\vee q)$.

Hence, option (A) is the correct answer.