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Question
Let R be the equivalence relation on the set Z of the integers given by R = { (a, b) : 2 divides a - b }.
Write the equivalence class [0].
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Solution
We have,
An equivalence relation, R = { (a, b) : 2 divides a - b }
If b=0, then a−b = a−0 = a
As, 2 divides a−b
And, the set of integers which are divided by 2 is { 0, ±2, ±4, ±6,... }
So, the equivalence class [0] = { 0,±2 ,±4 ,±6,... }
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