Question

On the set of natural numbers let R be the relation defined by a Rb if 2a + 3b = 30. Write down
the relation by listing all the pairs. Check whether it is
(i) reflexive (ii) symmetric (iii) transitive (iv) equivalence​

Answer 1

Answer:

N = {set of natural numbers} R = {(3, 8), (6, 6), (9, 4), (12, 2)} (i) (3, 3) ∉ R ⇒ R is not reflexive 2a + 3b = 3 3b = 30 – 2a b = (30 - 2a)/3 (ii) (3, 8) ∈ R (8, 3) ∉ R ⇒ R is not symmetric (iii) (a, b) (b, c) ∉ R ⇒ R is transitive (iv) ∴ It is not equivalence relationRead more on Sarthaks.com - https://www.sarthaks.com/900935/on-the-set-natural-numbers-let-the-relation-defined-by-arb-if-2a-3b-30-write-down-the-relation