• 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.

[see the comp182 logic section]

$A \rightarrow B$

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

Disjoined conclusions §

[see the comp182 logic section]

$P \rightarrow (Q \vee R)$

Sets §

[see the comp182 sets section]

Indexed families of sets §

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

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