The union of two equivalence relations on a set is not necessarily an equivalence relation on the set.

Define an equivalence relation.

If R and S are two equivalence relations on a set A then R nn S is also an equivalence relation on R.

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The intersection of two equivalence relations on a set A is an equivalence relation.

Let R and S be two equivalence relations on a set A Then : " " A. R uu S is an equvalence relation on A " " B. R nn S is an equirvalence relation on A " " C. R - S is an equivalence relation on A " " D. None of these

Statement-1: If R is an equivalence relation on a set A, then R^(-1) is also an equivalence relation. Statement-2: R = R^(-1) iff R is a symmetric relation.

If and and and are equivalence relations in a set A, show that R_(1)nn R_(2) is also an equivalence relation.

The inverse of an equivalence relation is an equvalence relation

Statement-1: The relation R on the set N xx N defined by (a, b) R (c, d) iff a+d = b+c for all a, b, c, d in N is an equivalence relation. Statement-2: The union of two equivalence relations is an equivalence relation.

Relation and Types of relations, Equivalence relation

Which of the following is an equivalence relation?