This shows that gof = IN
and fog = IY, which implies that f is invertible and g is the inverse of f Miscellaneous Examples
Example 18 If R1
 and R2 are equivalence relations in a set A, show that R1 ∩ R2 is
also an equivalence relation Solution Since R1
 and R2 are equivalence relations, (a, a) ∈ R1, and (a, a) ∈ R2 ∀ a ∈ A This implies that (a, a) ∈ R1 ∩ R2, ∀ a, showing R1 ∩ R2 is reflexive