Question

Write all distinct equivalence classes, if R ={(a, b) :(a-b) is a multiple of 2 and a, b belongs to Z}

Answer 1

Answer:

Solution

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R = (a,b) : 2 divides (a-b)

⇒(a−b) is a multiple of 2.

To find equivalence class 0, put b=0

So, (a−0) is a multiple of 2

⇒ a is a multiple of 2

So, In set z of integers, all the multiple

of 2 will come in equivalence

class {0}

Hence, equivalence class {0}={2x}

where x = integer (z)