Let R is the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) :2 divides ( a – b) }. Write the equivalence class [0].

Set A = {0, 1, 2, 3, 4, 5}

The equivalence relation on A is denoted by ;R

Set R = {(a, b):2 divides ( a b) }. ;R= { (0,2),(0,4),(1,3),(1,5).............(5,1)}

We must determine the equivalence class [0].

Put b = 0 to find equivalence class [0].

→ A = ois multiple of 2.

→ a is multiple of 2.

In the provided set, the multiples of 2 are 0, 2 and 4.

Therefore, the equivalence class {0} = {0, 2, 4}.