Let R be a relation defined on ℕ as a R b is 2 a + 3 b is a multiple of 5 , a , b ∈ ℕ . Then R is

Step-by-step solution

Given: R = a , b : 2 a + 3 b   is   divisible   by   5   for   a , b ∈ N Reflexive: 2 a + 3 a = 5 a is always divisible by 5 . So, a , a ∈ R Symmetric: Let a , b ∈ R i.e., 2 a + 3 b = 5 λ , where λ ∈ Z + . Now, 5 a + 5 b = multiple   of   5 ⇒ 2 a + 3 b + 2 b + 3 a = multiple   of   5 ⇒ 5 λ + 2 b + 3 a = multiple   of   5 ⇒ 2 b + 3 a = multiple   of   5 - 5 λ So, 2 b + 3 a is divisible