Question

Consider the following three statements:
$P:5$ is a prime number.
$Q:7$ is a factor of $192.$
$R:\text{L.C.M. of}5\text{and}7\text{is}35.$
Then the truth value of which one of the following statements is true?

• A. $(P\wedge Q)\vee (\sim R)$
• B. $(\sim P)\wedge (\sim Q\wedge R)$
• C. $P\vee (\sim Q\wedge R)$
• D. $(\sim P)\vee (Q\wedge R)$

Answer 1

The correct option is C $P\vee (\sim Q\wedge R)$

$P$ is true
$Q$ is false $\Rightarrow \sim Q$ is true
$R$ is true
$\Rightarrow \sim Q\wedge R$ is true
$\therefore P\vee (\sim Q\wedge R)$ is true