Question

(a). let A = { 1,2,3}. let R1 = { (1,1),(1,3),(3,1),(2,2),(2,1),(3,3)} R2= {(2,2),(3,1),(1,3), R3= {(1,3),(3,3)} find whether or not each of the relations R1,R2,R3 on is m (i) reflexive (ii) symmetric (iii) transitive. ​

Answer 1

Answer:

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Answer 2

Answer:

(i) R

1

= Reflexive :(a,a), (b,b), (c,c)∈R

Not symmetric :(a,b) ∈R but

(b,a)∈

/

R

1

Transitive (a,b) ∈R, (b,c)

inR

1

⇒ (a,c) ∈R

1

(ii) R

2

− Not reflexive (a,a) ∈RL

symmetric (a,b), (b,a) ∈R

2

(a,c),(c,a) ∈R

2

Not transitive

(a,b) ∈R

2

,(b,a) ∈R

2

but (a,a) ∈

/

R

2

(iii) R

3

Not reflexive (a,a) ∈

/

R

3

Not symmetric (a,b) ∈R

3

but (b,a) ∈

/

R

3

Not transitive (a,b) ∈R

3

(b,c) ∈R

3

but (a,c) ∈

/

R

3