Question

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

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

Answer 1

The correct option is B $p\to (p\vee q)$

Let us make the truth table for the given statements, as follows:
$\begin{array}{cccccc}p& q& p\vee q& q\to p& p\to (q\to p)& p\to (p\vee q)\\ T& T& T& T& T& T\\ T& F& T& T& T& T\\ F& T& T& F& T& T\\ F& F& F& T& T& T\end{array}$
From table we observe
$p\to (q\to p)$ is equivalent to $p\to (p\vee q)$