## Contrapositive

$$\not$$B $$\rightarrow$$ $$\not$$A $$\equiv$$ A $$\rightarrow$$ B

### When to use Contrapositive:

• when the statement Not A or Not B gives useful information
• if A or B have conditions that are only one of two possibilities (ex. odd or even)

## Proof by Contradiction

A ∧ $$\not$$A must be false. “A ∧ $$\not$$A must be true” is a Contradiction

### When to use Contradiction:

• when it is difficult to use direct method
• when NOT B gives more useful information than B