Question:
Let R be the equivalence relation on the set Z of the integers given by R = {(a, b) : 2 divides a
[NCERT EXEMPLAR]
Solution:
We have,
An equivalence relation, R = {(a, b) : 2 divides a
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 $\{0, \pm 2, \pm 4, \pm 6, \ldots\}$
So, the equivalence class $[0]=\{0, \pm 2, \pm 4, \pm 6, \ldots\}$
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