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Please show the proof that: Either [a]=[b] or [a] *union* [b] = empty set this will...

Please show the proof that:

Either [a]=[b]
or [a] *union* [b] = empty set

this will be proof by contrapositibe but please show work:


theorem: suppose R is an equivalence of a non-empty set A. let a,b be within A

then [a] does not equal [b] implies that [a] *intersection* [b] = empty set
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