Question

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

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

Answer 1

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

Truth Table for given statements is as follows:
$\begin{array}{cccccccccccc}p& q& q\to p& p\to (q\to p)& p\to q& p\to (p\to q)& q\vee p& p\wedge q& p\leftrightarrow q& p\to (q\vee p)& p\to q\wedge p& p\to (p\leftrightarrow q)\\ T& T& T& T& T& T& T& T& T& T& T& T\\ T& F& T& T& F& F& T& F& F& T& F& F\\ F& T& F& T& T& T& T& F& F& T& T& T\\ F& F& T& T& T& T& F& F& T& T& T& T\end{array}$
$\therefore \text{using truth table}p\to (q\to p)$ is logically equivalent to $p\to (q\vee p)$