Question

Let R = {(1,2), (2, 1), (1, 1)} be a relation on A = {1,2}. Then Ris
a) Reflexive b) symmetric only c) transitive d) None of these​

Answer 1

b) symmetric only

draw universe relation diagram

Answer 2

Given:

R =  {(1,2), (2, 1), (1, 1)}, and

A = {1,2}.

To Find:

R is:  a). Reflexive, b). symmetric only, c). transitive, or d). None of these.

Solution:

For A, Reflexive: If a relation has {(x, y)} as its element, then it should also have {(x, x),(y, y)} as its elements. This is not the case for the given relation.

​For B, Symmetric: If a relation has (x, y) as its element, then it should also have {(y, x)} as its element. This is also not the case for the given relation.

For C, Transitive: If a relation has {(x, y),(y, z)} as its elements, then it should also have {(x, z)} as its element. This case is relevant for the given relation.

Hence, the correct option is Option C: Transitive.