Question

Assertion (A): The relation R = (x, y) : (x + y) is a prime number and x, y in N is not a reflexive relation. 
Reason (R): The number \( 2n \) is composite for all natural numbers \( n \).
 

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

A relation is reflexive if every element relates to itself; check this condition for all elements.

Answer 1

The Correct Option is C

Step 1: Analyze Assertion (A)
For \( R \) to be reflexive, \( (x, x) \) must belong to \( R \) for all x in N . This means \( x + x = 2x \) must be a prime number. However, for \( x>1 \), \( 2x \) is not a prime number as it is divisible by \( 2 \). Therefore, \( R \) is not reflexive, and Assertion (A) is true. 
Step 2: Analyze Reason (R)
The Reason states that \( 2n \) is composite for all \( n \). This is false because when \( n = 1 \), \( 2n = 2 \), which is a prime number. Therefore, Reason (R) is false. 
Step 3: Conclusion
Since Assertion (A) is true and Reason (R) is false, the correct answer is option (C).