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Math 3450 - Homework # 3 Equivalence Relations and …

If x 6= 0, then the equivalence class of x is x = f x;xg. The equivalence class of 0 is 0 = f0g. 3.Consider the set S = Z where x ˘y if and only if 2j(x+ y). (a)List six numbers that are related to x = 2. Solution: 2 ˘( 4) since 2j(2 + ( 4)). 2 ˘( 2) since 2j(2 + ( 2)). 2 ˘(0) since 2j(2 + (0)). 2 ˘(2) since 2j(2 + (2)). 2 ˘(4) since 2j(2 ...

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