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