Problem-44

Problem-44

For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.

a) {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}

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

c) {(1,4),(4,1)}

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

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

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

 

Solution

 

a) {(2,2),(2,3),(2,4),(3,2),(3,3),(3,4)}

Transitive

 

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

Transitive

Reflexive

Symmetric

 

c) {(1,4),(4,1)}

Symmetric

 

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

Antisymmetric

 

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

Antisymmetric

Reflexive

Symmetric

Transitive

 

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

None of the above properties.

Leave a Reply