Q. 534.0( 2 Votes )

# State 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.

Answer :

False

Given that, R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}

Now,

R is not reflexive ∵ (1,1),(2,2) ∉ R.

R is symmetric ∵ (3,1) ∈ R ⇒ (1,3) ∈ R

R is not transitive ∵ (1,3) ∈ R and (3,1) ∈ R but (1,1) ∉ R.

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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