Question

On the set of natural numbers let R be the relation defined by aRb if 2a+3b=30.Write down the relation and check whether it is
1)reflexive 2)symmetric 3)transitive

Answer 1

Answer:

R is not reflexive

R is not symmetric

R is transitive

Step-by-step explanation:

Given:

aRb if 2a+3b=30

Then,

R= { (3,8), (6,6), (9,4), (12,2) }

1. For each n∈N, (n,n) ∉ R except (6,6)

Hence, R is not reflexive

2. (3,8) ∈ R but (8,3) ∉ R

R is not symmetric

3. We cannot find two elements (a,b) and (b,c) such that (a,c) ∉ R

Hence R is transitive

Also, R is not an equivalance relation.