Ohio State University Mathematics Prove Proof by Cases Questions

Overview

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

Prove by cases:

1) Statement: If 𝒏 ∈ ℤ, then 𝒏

𝟐 + 𝟑𝒏 + 𝟓 is an odd integer.

Proof:

2) Statement: If 𝒏 ∈ ℤ, then 𝒏

𝟑 − 𝒏 is even.

Prove:

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

Statement: If 𝟔𝒙 − 𝟐 is odd, then 𝟐𝒙 + 𝟑 is even