Show that the relation $R$ in the set $A= \{1,2,3,4,5\}$given by $R = \{(a, b) : |a – b| \,is\, even \}$, is an equivalence relation. Show that all the elements of $\{1, 3, 5\}$ are related to each other and all the elements of $\{2, 4\}$ are related to each other. But no element of $\{1, 3, 5 \}$ is related to any element of $\{2, 4\}$.

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