If I have an equivalence relation acting on all integers (Z): a ~ b if any only if 3a + b is a multiple of 4, then here is what I think the quotient set is:(adsbygoogle = window.adsbygoogle || []).push({});

The equivalence class of 0 = {x belongs to Z | x ~ 0} = {x | 3x = 4n for some integer n}. (The set would look like {0, 4, 8, 12, 16...}.)

The equivalence class of 1 = {x belongs to Z | x ~ 1} = {x | 3x + 1 = 4n for some integer n}. (The set would look like {1, 5, 9, 13, 17...}.)

The equivalence class of 2 = {x belongs to Z | x ~ 2} = {x | 3x + 2 = 4n for some integer n}. (The set would look like {2, 6, 10, 14, 18...}.)

The equivalence class of 3 = {x belongs to Z | x ~ 3} = {x | 3x + 3 = 4n for some integer n}. (The set would look like {3, 7, 11, 15, 19...}.)

So based on that, I conclude that there are 4 elements in the quotient set. Each element contains one of the sets above.

Am I accurate here? Thanks.

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# Guessing the quotient of

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