Q. 1C4.0( 137 Votes )

# Relation R in the set A = {1, 2, 3, 4, 5, 6} as

R = {(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.

Rate this question :

Fill in the blanks in each of the

Let the relation R be defined on the set

A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^{2} – b^{2}| < 8}. Then R is given by _______.

State True or False for the statements

Every relation which is symmetric and transitive is also reflexive.

Mathematics - ExemplarState True or False for the statements

Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Mathematics - ExemplarState True or False for the statements

An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

Mathematics - Exemplar