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Question

Ifp:4 is an even prime number,q:6 is a divisor of 12and r: the HCF of 4and 6is2, then which one of the following is correct?


A

(pq)

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B

(pq)~r

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C

~(qr)p

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D

~p(qr)

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E

p(qr)

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Solution

The correct option is D

~p(qr)


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 2or4.

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 6×2=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 is2.

The prime factorization of 4and6 are 2×2and2×3 respectively.

Then the HCF is 2.

Therefore, r is also a true statement.

From this, we can conclude that the answer is ~p(qr).

Hence, option D is correct.


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