The following exercises describe a relation with certain properties. For each, say whether it is possible for a relation R ⊆ A × A to simultaneously have all of the stated properties. If so, describe...

The following exercises describe a relation with certain properties. For each, say whether it is possible for a relation

R ⊆ A × A to simultaneously have all of the stated properties. If so, describe as precisely as possible what structure the

relation R must have. If not, prove that it is impossible.

1 Is it possible for R to be simultaneously symmetric, transitive, and irreflexive?

2 Is it possible for R to be simultaneously transitive and a function?