Question

Give an example to show that the union of two equivalence relations on set A need not to be an Equivalence relations on set A​

Answer 1

Explanation:

However 7-(-5) = 12, which is neither divisible by 5 nor by 7. Hence, we have (7,−5)∉R1 and (7,−5)∉R2⇒(7,−5)∉R1⋃R2. ... Since R1⋃R2 is not transitive, it is not an equivalence relation. Hence the union of two equivalence relations on a set may not be an equivalence relation.

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