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Relation and Types of relations, Equival...

Relation and Types of relations, Equivalence relation

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Define an equivalence relation.

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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.

The inverse of an equivalence relation is an equvalence relation

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In the set Z of all integers, which of the following relation R is not an equivalence relation?

Let O be the origin.We define a relation between two points P and Q in a plane if OP=OQ. Show that the relation,so defined is an equivalence relation.

Let O be the origin.We define a relation between two points P and Q in a plane if OP=OQ. Show that the relation,so defined is an equivalence relation.