Question

If$p:4$ is an even prime number,$q:6$ is a divisor of $12$and $r$: the HCF of $4$and $6$is$2$, then which one of the following is correct?

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

Answer 1

The correct option is D

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

Explanation for the correct option.

As per the first statement which is

$p:4$ is an even prime number.

We know that an even number can never be a prime number as it will always be divisible by $2\text{or}4$.

Therefore, $p$ is a false statement as $4$ is not a prime number.

Now, the second statement which is

$q:6$ is a divisor of $12$.

We know that $6\times 2=12$ then $6$ is a divisor of $12$

Therefore, $q$ is a true statement

Finally, the third statement that is

$r$: the HCF of $4$ and $6$ is$2$.

The prime factorization of $4\text{and}6$ are $2\times 2\text{and}2\times 3$ respectively.

Then the $\text{HCF}$ is $2$.

Therefore, $r$ is also a true statement.

From this, we can conclude that the answer is $~p\vee (q\wedge r)$.

Hence, option D is correct.