Question

on the set of natural numbers let R be the relation defined by aRb if 2a+2b=3b .write down the relation by listing all the pairs check whether it is​

Answer 1

Answer:

The Relation is not reflexive.

The Relation is not symmetric.

The Relation is not transitive.

Step-by-step explanation:

Complete question:

on the set of natural numbers let R be the relation defined by aRb if 2a+2b=3b .write down the relation by listing all the pairs check whether it is​ reflexive,symmetric and transitive.

Solution:

aRb if 2a+3b=30

since when

a=3 b=8

2×3+3×8=30

⇒ (3,8) ∈ R

Similarly

(6,6)∈R  

(9,4)∈R

(12,2)∈R

Thus the set of ordered pairs that satisfy the given condition given below

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

Now

The relation is reflexive if

x R x for all (x,x) ∈ R

since only

6 R 6 So the relation is not reflexive.

Since

The relation is symmetric if (a,b) ∈ R then (b,a) ∈ R

In our case

(3 , 8) ∈ R but (8 , 3) ∉ R

So

The relation is not symmetric.

Now

The relation is transitive if (a , b) ∈ R and (b,c) ∈ R then (a , c) ∈ R

In our case

There exist no such pairs so the relation is not transitive