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Determine whether or not the following is an equivalence relation on N. If it is not,...

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Advance Math

Determine whether or not the following is an equivalencerelation on N. If it is not, determine which property fails. If itis, prove it.

(a) x ? y if and only if x|y (x evenly divides y).

(b) x ? y if and only if the least prime dividing x is thesame as the least prime dividing y. In this case, instead if usingN, use the set A = {2,3,4,5,...}.

(c) x?yifandonlyif|x?y|<5.

(d) x?yifandonlyifx=4.

2. Prove that x ? y if and only if sin x = sin y is anequivalence relation on R. What is the equivalence class of[?]?

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