Question

Assertion(A): The relation R = {(x,y) : (x +y) is a prime number and x, y ∈ N} is not a reflexive relation.

Reason (R): The number ‘2n’ is composite for all natural numbers n.

Options

• Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of the Assertion (A).

• Assertion (A) is true, but Reason (R) is false.

• Assertion (A) is false, but Reason (R) is true.

Answer 1

Assertion (A) is false, but Reason (R) is true.

Explanation:

Assertion: R = {(x, y) : (x + y) is a Prime Number and x, y ∈ N}

Reflexive: For (1 + 1) is Prime Number (1, 1) ∈ R

For (2 + 2) is not prime number (2, 2) ∈ R So, R is not reflexive.

Reason: A composite number is a natural number or positive integer that has more than two factors.

So; (2n) is more than two factor and it is not prime.