Question

35. Show that the relation R in the set Z of integers, given by
R = {(a,b): 3 divides a – b} is an equivalence relation. Hence find the
equivalence classes of 0, 1 and 2.​

Answer 1

Answer:

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)