Show that the relation R on Z × Z defined by (a, b) R (c, d) if and only if a + d = b + c is an equivalence relation. Note: A relation on a set A is called an equivalence relation if it is reflexive, symmetric, and transitive.
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A relation R on defined by iff
we see that,
therefore R is reflexive relation
Let (a, b) R(c, d)
Therefore R is symmetric relation.
Therefore R is transitive relation.
Therefore R is an equivalence relation.