Question

Let A={1 , 2, 3, 4,5, 6} and let `S=P(A)`, the power set of A How many equivalence classes are there ? List one element from each equivalence class​

Answer 1

Answer:

0,2,4

Explanation:

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

R be the equivalence relation on A.

Set R={(a,b)2divides(a−b)}

We have to find equivalnce class [0]

To find equivalence class {0},put b=0

⇒a−0 is multiple of 2 .

⇒ a is multiple of 2.

Multiples of 2 in given set are 0,2 and 4 .

Hence equivalence class {0}={0,2,4}