Proof by Cases

I need help with a Mathematics question. All explanations and answers will be used to help me learn.

Prove by cases:

1) Statement: If ∈ ℤ, then

+ + is an odd integer.

Proof:

2) Statement: If ∈ ℤ, then

− is even.

Prove:

3) Prove the following statement by Proof by Contrapositive, and Proof by Contradiction:

Statement: If − is odd, then + is even

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