Question

Consider the following three statements:
$p:4$ and $7$ are coprimes.
$q:$ Every function on a set $A$ is a relation on $A$.
$r:6$ divides $3$.
Then the truth value of which of the following Boolean expressions is false?

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

Answer 1

The correct option is C $\sim p\wedge (q\vee \sim r)$

$p$ is true, $q$ is true and $r$ is false.

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

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

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

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