11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following: (a) For each a, b e A, a × b if and only if [a] N [b] = Ø. (b) For each a, b e A, if [a] # [b], then...

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11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove<br>each of the following:<br>(a) For each a, b e A, a × b if and only if [a] N [b] = Ø.<br>(b) For each a, b e A, if [a] # [b], then [a] N [b] = Ø.<br>(c) For each a, b e A, if [a] N [b] # Ø then [a] = [b].<br>

Extracted text: 11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following: (a) For each a, b e A, a × b if and only if [a] N [b] = Ø. (b) For each a, b e A, if [a] # [b], then [a] N [b] = Ø. (c) For each a, b e A, if [a] N [b] # Ø then [a] = [b].

Jun 05, 2022

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11. Let A be a nonempty set and let ~ be an equivalence relation on A. Prove each of the following: (a) For each a, b e A, a × b if and only if [a] N [b] = Ø. (b) For each a, b e A, if [a] # [b], then...

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