Question

Let $p : 57$ is an odd prime number,
$\quad \, q : 4$ is a divisor of $12$
$\quad$ $r : 15$ is the $LCM$ of $3$ and $5$
Be three simple logical statements. Which one of the following is true?

• A. $p ∨ (∼ q ∧ r )$
• B. $∼ p ∨ (q ∧ r )$
• C. $( p ∧ q)v ∼$
• D. $( p ∨ q)∧ ∼ r$
• E. $∼ p ∧ (∼ q ∧ r )$

Answer 1

Answer: (B)

$p: 57$ is an odd prime number
$q: 4$ is a divisor of 12
$r: 15$ is the LCM of 3 and 5 .
Then, $p$ is $F$
$q$ is $T$
$r$ is $T$
By the given options
$\sim p \vee(q \wedge r)$
$=\sim F \vee(T \wedge T)=T \vee(T)=T$