Question

Let R be the relation defined on the set S =
{2, 3, 4, 5} by the open sentence
X-y is divisible by 3 then R =
​

Answer 1

ANSWER

aRa is positive as a+2a=3a is divisible by 3

Hence reflexive

If aRb is positive a+2b is divisible by 3

Hence 3a+3b−(2a+b) is divisible by 3

⇒2a+b is divisible by 3

ie aRb is positive

⇒bRa is positive hence symmetric

aRb,bRc is a+2b,b+2c divisible by 3

⇒a+2b+b+2c divisible by 3

⇒a+3b+2c divisible by 3

So a+2c divisible by 3 hence transitive

So it is an equivalence relation.

Answer 2

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It is eqivalence reaction.