Exercise 1

Consider the statement “for all integers $a$ and $b$, if $a + b$ is even, then $a$ and $b$ are even”

1. Write the contrapositive of the statement.

2. Write the converse of the statement.

3. Write the negation of the statement.

4. Is the original statement true or false? Prove your answer.

5. Is the contrapositive of the original statement true or false? Prove your answer.

6. Is the converse of the original statement true or false? Prove your answer.

7. Is the negation of the original statement true or false? Prove your answer.