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.