For each of these relations on the set {21, 22, 23, 24}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.

i. { (22, 22), (22, 23), (22, 24), (23, 22), (23, 23), (23, 24) }

ii. { (21, 21), (21, 22), (22, 21), (22, 22), (23, 23), (24, 24) }

Question

Mary Fischer

Mathematics

18 February, 09:34

For each of these relations on the set {21, 22, 23, 24}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive.

i. { (22, 22), (22, 23), (22, 24), (23, 22), (23, 23), (23, 24) }

ii. { (21, 21), (21, 22), (22, 21), (22, 22), (23, 23), (24, 24) }

+5

Answers (2)

Know the Answer?

Mercedes Harvey · Answer 1

Step-by-step explanation:

I. { (22,22), (22,23), (22,24), (23,22), (23,23), (23,24) }

Reflexive : True because we see the pairs (22,22), (23,23) ...

Symmetrix : NO, as we see the pairs (22,24) BUT NOT (24,22)

Transitive : YES, As we see (22,22) and (22, 24), we see the pairs (22,24)

Antisymmetric : NO

II) { (21,21), (21,22), (22,21), (22,22), (23,23), (24,24) }

Reflexive : True because we see the pairs (22,22), (23,23) (21,21)

Symmetrix : Yes, as we see the pairs (21,22) AND (22,21)

Transitive : YES,

Antisymmetric : NO

Kaleigh Wood · Answer 2

Step-by-step explanation:

I. { (22,22), (22,23), (22,24), (23,22), (23,23), (23,24) }

Reflexive : True because we see the pairs (22,22), (23,23) ...

Symmetrix : NO, as we see the pairs (22,24) BUT NOT (24,22)

Transitive : YES, As we see (22,22) and (22, 24), we see the pairs (22,24)

Antisymmetric : NO