Question

let a={1,2,3,4,5}. construct a relation of not reflexive, symmetric,transitive​

Answer 1

(i) we define a relation R

1

as

R

1

={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(1,3)}

Then it is easy to check that R

1

is reflexive, transitive but not symmetric. Students are advised to write other relations of this type.

(ii) Define R

2

as: R

2

={(1,2),(2,1)}

Ti is clear that R

2

is symmetric but neither reflexive nor transitive. Write other relations of this type.

(iii) We define r

3

as follows:

R

3

={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)}.

Then evidently R

3

is reflexive, symmetric and transitive, that is, R

3

is an equivalence relation on A.

(1, 2) ∈R

3

,(2,1)∈R

3

⇒(1,1)∈R

3