Shreyas’ Notes

# MATH 302

• direct proof

Assume $p$ is true, then show that $q$ must also be true.

• proof of contrapositive

Assume $q$ is false, then show that $p$ must also be false.

• proof by contradiction

Assume $p$ is true and $q$ is false. Then show that this leads to a contradiction.

a statement is a sentence that is either true or false.

$A \rightarrow B$

• Converse: $B \rightarrow A$
• Contrapositive: $\neg B \rightarrow \neg A$

### Disjoined conclusions §

$P \rightarrow (Q \vee R)$

## Sets §

### Indexed families of sets §

$x \in \bigcup_{n=1}^{\infty} S_n \leftrightarrow \exists n_x \in \mathbb{N} : x \in S_{n_x}$

$x \in \bigcap_{n=1}^{\infty} S_n \leftrightarrow \forall n \in \mathbb{N} : n \in S_{n_x}$