1. Identify all relations R on {0, 1} that are transitive. 2. Of the transitive relations on {0, 1} from Exercise 8.89, which are also reflexive and symmetric?   Exercise 8.89 The following exercises...

1. Identify all relations R on {0, 1} that are transitive.

2. Of the transitive relations on {0, 1} from Exercise 8.89, which are also reflexive and symmetric?

Exercise 8.89

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?