question_answer

Let\[R=\{(1,3),(4,2),(2,4),(2,3),(3,1)\}\]be a relation on the set\[A=\{1,2,3,4\}\]. The relation R is

A) a function       

B) transitive                            

C) not symmetric   

D)       reflexive

Correct Answer: C

Solution :

A correspondence which is one-one or many-one is called a function, a one to many or many to many correspondence cannot be a function. Let R = {(1, 3), (4,2), (2,4), (2,3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}, then Since,andso R is not a function. Since,andbut. So, R is not transitive. Since,but,so R is not symmetric. Since,,so R is not reflexive. Hence, the option (c) is correct. NOTE A relation which is not symmetric, is known as anti-symmetric relation.