Let φ: S→T be any map from S into T, and define a relation ∼ on S by a∼b if and only if φ(a) =φ(b). a) Show that ∼ is an

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Let φ: S→T be any map from S into T, and define a relation ∼ on
S by a∼b if and only if φ(a) =φ(b).
a) Show that ∼ is an equivalence relation on S.
b) Suppose φ is one-to-one. Describe the equivalence classes of
∼.
c) Suppose instead that φ is constant. Describe the equivalence
classes of ∼.