Question

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

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

Answer 1

Answer: (B)

$\sim p\vee (q\wedge r)$

$p:57$ is an odd 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

$\sim p\vee (q\wedge r)$
$=\sim F\vee (T\wedge T)=T\vee \left(T\right)=T$