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Elementary logic and set theory

Table of contents: Logical operations - Sets - Set operations

Logical operations

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

Sets

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Symbol: Set {}\left\{\ldots\right\} Set with given elements
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Symbol: SetBuilder {f ⁣(x):P ⁣(x)}\left\{ f\!\left(x\right) : P\!\left(x\right) \right\} Set comprehension

Set operations

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

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

2019-07-15 23:42:41.550119 UTC