question_answer 15)

Let R be the relation in the set of {1, 2, 3, 4} given by R = {(1, 2,), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer : (A) R is reflexive and symmetric but not transitive. (B) R is reflexive and transitive but not symmetric. (C) R is reflexive and transitive but not symmetric. (D) R is an equivalence relation.  

Answer:

Let A = {1, 2, 3, 4}       R = {(1, 2), (2, 2),(1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}       Clearly R is reflexive and transitive.       As (1, 2)but (2, 1)        is not symmetric.        is correct.