Question

If p, q, r have truth values T, F, T respectively, then which of the following is $\text{True}$?

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

Answer 1

The correct option is D $q\to (p\wedge r)$

Since, p is true and q is false.

$\therefore p\to q$ has truth value F.
Statement r has truth value T.

$\therefore (p\to q)\wedge r$ has truth value F.

Also, $(p\to q)\wedge \sim r$ has truth value F.

Now, $p\wedge q$ has truth value F and $p\vee r$ has truth value T.

$\therefore (p\wedge q)\wedge (p\vee q)$ has truth value F.
As, $p\wedge r$ has truth value T.

Therefore, $q\to (p\wedge r)$ has truth value T.