# Elementary logic and set theory

## Logical operations

Symbol: Not $\operatorname{not} \left(x\right)$ 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
Symbol: SetBuilder $\left\{ f\!\left(x\right) : P\!\left(x\right) \right\}$ Set comprehension

## Set operations

Symbol: Cardinality $\# S$ Set cardinality
Symbol: PowerSet $\mathscr{P}\!\left(S\right)$ 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.

2019-09-19 20:12:49.583742 UTC