Consider the following relation Ron a set A R={ (a, a) (a, b) (b, a) (b, b) (b, c) (cc) } Consider the following statements Stat 1: R is an equivalence relation Stat 2: R is not an equivalence relation because it is not transitive Stat 3: R is not an equivalence relation because it is not symmetric Stat 4: Adding just one ordered pair to R can make the new relation equivalence relation Choose the correct statements a) Stat 1 is True and Stat 4 is true b) Stat 2 is true c) Stat 4 is false d) Stat 3 is false d) Stat 3 is false a) Stat 1 is True and Stat 4 is true b) Stat 2 is true

Answer with Step-by-step explanation:

We are given that a relation on set A

R={ (a, a), (a, b), (b, a), (b, b), (b, c), (c, c) }

We have to tell which statement is true about the given relation.

We know that if relations is reflexive, symmetric and transitive then the relation is called equivalence relation.

Reflexive:if (a, a) is present in the given relation for every element a belongs to A.

Symmetric : If (a, b) are present in the relation the (b, a) is also present in the given relation for every ordered pair (a, b) belongs to R.

Transitive: If (a, b) and (b, c) are present in the given relation then (c, a) is also present in the given relation.

Therefore, given relation is reflexive.

Given relation is not symmetric and not transitive because (c, b) and (c, a) are not present in the given relation. Therefore, relation is not equivalence.

Therefore,

Option

(a) Stat 2 : true.

(c) Stat 4: False Because we need two ordered pair to make the equivalence relation.