Question

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is 

(i) reflexive 

(ii) symmetric 

(iii) transitive 

(iv) equivalence

Answer 1

Set of all natural numbers aRb if a + b ≤ 6 

R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 2), (5, 1)}

(i) (5, 1) ∈ R but(5, 5) ∉ R 

It is not reflexive 

(ii) aRb ⇒ bRa ⇒ It is symmetric

(iii) (4, 2), (2, 3) ∈ R ⇒ (4, 3) ∉ R 

∴ It is not transitive 

(iv) ∴ It is not an equivalence relation