Exercise 19.

Suppose \(f:X \to Y\) is a function. Which of the following are possible? Explain.

1. \(f\) is injective but not surjective.

2. \(f\) is surjective but not injective.

3. \(|X| = |Y|\) and \(f\) is injective but not surjective.

4. \(|X| = |Y|\) and \(f\) is surjective but not injective.

5. \(|X| = |Y|\text{,}\) \(X\) and \(Y\) are finite, and \(f\) is injective but not surjective.

6. \(|X| = |Y|\text{,}\) \(X\) and \(Y\) are finite, and \(f\) is surjective but not injective.