# Elementary logic and set theory

Table of contents: Logical operations - Sets - Set operations

## Logical operations

Symbol: Not $\operatorname{not} x$ Logical not
Symbol: And $x \;\mathbin{\operatorname{and}}\; y$ Logical and
Symbol: Or $x \;\mathbin{\operatorname{or}}\; y$ Logical or
Symbol: Equivalent $\left(x\right) \iff \left(y\right)$ Logical equivalence
Symbol: Implies $\left(x\right) \implies \left(y\right)$ Logical implication

## Sets

Symbol: Set $\left\{\ldots\right\}$ Set with given elements

## Set operations

Symbol: Cardinality $\# S$ Set cardinality
Symbol: PowerSet $\mathscr{P}(S)$ Power set
Symbol: Union $S \cup T$ Set union
Symbol: Intersection $S \cap T$ Set intersection
Symbol: SetMinus $S \setminus T$ Set difference
Symbol: Element $x \in S$ Set membership
Symbol: NotElement $x \notin S$ Set non-membership
Symbol: Subset $S \subset T$ Strict subset
Symbol: SubsetEqual $S \subseteq T$ Subset

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC