Let R be a relation over the set N×n and it is defined by (a, b) R (c, d) ⇒ a+ d = b + c. Then, R is
Options:
A .  
reflexive only
B .  
symmetric only
C .  
transitive only
D .  
an equivalence relation
Answer: Option D : D (a, b) R (a, b) because a + b = b + a. So, r is reflexive. (a, b)R (c, d) ⇒ a+d = b+c ⇒ c+b = d+a ⇒ (c,d) R (a,b) So, R is symmetric. (a, b) R (c, d) and (c, d) R (e, f) ⇒ a + d = b + c, c + f = d + e Adding, a + d + c + f = b + c + d +e ⇒ a + f = b + e ⇒ (a, b) R (e, f). ∴ R is transitive.
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