(2)

It is given that .

An equivalence relation is reflexive, symmetric and transitive.

The smallest equivalence relation containing is given by,

Now, we are left with only four pairs i.e., , and .

If we add any one pair say to , then for symmetry we must add .

Also, for transitivity we are required to add and .

Hence, the only equivalence relation (bigger than ) is the universal relation.

This shows that the total number of equivalence relations containing is two.

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