Q. 1C4.0( 137 Votes )

# Relation R in the set A = {1, 2, 3, 4, 5, 6} asR = {(x, y) : y is divisible by x}

Answer :

It is given that relation R in the set A = {1, 2, 3, 4, 5, 6} as

R = {(x, y) : y is divisible by x}

We know that any number (x) is divisible by itself.

(x,x) ϵ R

R is reflexive.

Now, (2,4) ϵ R but (4,2) R.

R is not symmetric.

Let (x,y), (y,z) ϵ R. Then, y is divisible x and z is divisible by y.

z is divisible by x.

(x,z) ϵ R

R is transitive.

Therefore, R is reflexive and transitive but not symmetric.

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