Let R be a relation on N × N defined by (a, b) R (c, d) if and only if a + d = b + c. This relation is:

Let R be a relation on N × N defined by (a, b) R (c, d) if and only if a + d = b + c. This relation is:

• A. Reflexive and symmetric only
• B. Symmetric and transitive only
• C. Reflexive and transitive only
• D. An equivalence relation

Answer: D) An equivalence relation

Explanation: Reflexive: a+b = b+a. Symmetric: a+d = b+c → c+b = d+a → (c,d) R (a,b). Transitive: a+d=b+c and c+f=d+e. Adding them: a+d+c+f = b+c+d+e → a+f = b+e → (a,b) R (e,f). Thus, it's an equivalence relation.