Question

If R= {0,1,2,3), S = {0,2,4), then find:
(a) RS
(b)S/R​

Answer 1

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GIVEN :

R= {0,1,2,3}, S = {0,2,4}

(a) R/S

ANS:. ( we have to write elements which are present in the Set of R but not in the Set of S )

As we look into , we find that 1 and 3 is present in the Set of R but not in the Set of S.

So, R/S ={1,3}

(b) S/R

ANS:

Just like above note , 4 is present in the Set of S but not in the Set of R.

So, S/R = {4}

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Answer 2

Answer:

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}