Suppose that R ⊆ A × B and T ⊆ B × C are relations. Prove the following: 1. If R and T are both functions, then T ◦ R is a function too. 2. If R and T are both one-to-one functions, then T ◦ R is...

Suppose that R ⊆ A × B and T ⊆ B × C are relations. Prove the following:

1. If R and T are both functions, then T ◦ R is a function too.

2. If R and T are both one-to-one functions, then T ◦ R is one-to-one too.

3. If R and T are both onto functions, then T ◦ R is onto too.