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