Question

Let a={1,2,3} and consider the relation r={(1,1),(2,2),(3,3) ,(1,2),(2,3),(1,3)}. Then r is _____

Answer 1

Answer:

Hence, given relation 'r' is reflexive, transitive but not symmetric

Step-by-step explanation:

Given,

• a = {1,2,3}
• r={(1,1),(2,2),(3,3),(1,2),(2,3)(1,3)}

Reflexive:-

In the relation 'r' has (1,1),(2,2),(3,3)

which shows the property of Reflexive

(a,a) ∈ r

Hence, relation 'r' is reflexive

Symmetric:-

Relation 'r' has (1,2)∈r but (2,1)∉r

Hence, 'r' is not symmetric.

Transitive:-

Relation 'r' has (1,2)∈R, (2,3)∈r also (1,3)∈r

This implies that 'r' is transitive