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Math Help - Equality

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    Equality

    Prove that equality is the smallest equilivence relation on a set A.
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    Quote Originally Posted by Chris11 View Post
    Prove that equality is the smallest equilivence relation on a set A.
    Given a set A then \Delta _A  = \left\{ {(x,x):x \in A} \right\} is known as the diagonal.
    Also  \Delta _A is also the equality relation.
    Also if \mathcal{E} is an equivalence on A then it must be the case that \Delta_A\subseteq\mathcal{E}.
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