Suppose a relation R = {(3, 3), (5, 5), (5, 3), (5, 5), (6, 6)} on S = {3, 5, 6}. Here R is known as _________a.equivalence relationb.symmetric relationc.transitive relation’’d.reflexive relat

To determine the type of relation R, we need to check the properties of each type of relation:

a. Equivalence relation: A relation is an equivalence relation if it is reflexive, symmetric, and transitive.

b. Symmetric relation: A relation is symmetric if for all (a, b) in R, (b, a) is also in R.

c. Transitive relation: A relation is transitive if for all (a, b) in R and (b, c) in R, (a, c) is also in R.

d. Reflexive relation: A relation is reflexive if for all a in S, (a, a) is in R.

Now, let's check each property for the given relation R:

1. Reflexive: For all a in S = {3, 5, 6}, we have (a, a) in R. So, R is reflexive.

2. Symmetric: For all (a, b) in R, we need to check if (b, a) is in R. We have (5, 3) in R but we don't have (3, 5) in R. So, R is not symmetric.

3. Transitive: For all (a, b) in R and (b, c) in R, we need to check if (a, c) is in R. We don't have any such pairs in R where (a, b) and (b, c) are in R but (a, c) is not in R. So, R is transitive.

Therefore, the given relation R is a reflexive and transitive relation, but it is not an equivalence relation because it is not symmetric.