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Set Theory and Logic Symbols Cheat Sheet
Copy membership, subset, union, intersection, quantifier, implication, and logical operator symbols.
How to use this sheet
Use membership symbols for elements and subset symbols for sets. Keep implication direction and quantifier scope visible.
| Symbol | Name and meaning | LaTeX | Unicode |
|---|---|---|---|
| Element OfStates that an object belongs to a set. | \in |
U+2208 |
|
| Not an Element OfStates that an object does not belong to a set. | \notin |
U+2209 |
|
| Subset / Proper SubsetOften denotes a proper subset, although conventions vary between textbooks. | \subset |
U+2282 |
|
| Subset or Equal ToStates that every element of the left set is in the right set, allowing equality. | \subseteq |
U+2286 |
|
| Superset OfIndicates that the left set contains the right set. | \supset |
U+2283 |
|
| Superset Of or Equal ToIndicates that every element of the right set is in the left set. | \supseteq |
U+2287 |
|
| UnionForms the set of elements that appear in either set. | \cup |
U+222A |
|
| IntersectionForms the set of elements shared by both sets. | \cap |
U+2229 |
|
| Empty SetRepresents the unique set containing no elements. | \varnothing |
U+2205 |
|
| Set MinusRepresents elements in one set that are not in another. | \setminus |
U+2216 |
|
| For AllUniversal quantifier meaning that a statement holds for every allowed value. | \forall |
U+2200 |
|
| There ExistsExistential quantifier meaning that at least one value satisfies a statement. | \exists |
U+2203 |
|
| There Does Not ExistStates that no object satisfies a stated property. | \nexists |
U+2204 |
|
| Logical AndConjunction that is true only when both component statements are true. | \land |
U+2227 |
|
| Logical OrInclusive disjunction that is true when at least one component statement is true. | \lor |
U+2228 |
|
| Logical NotNegates a proposition or Boolean value. | \neg |
U+00AC |
|
| ImpliesIndicates logical implication from a premise to a conclusion. | \Rightarrow |
U+21D2 |
|
| If and Only IfIndicates that two statements imply each other and are logically equivalent. | \Leftrightarrow |
U+21D4 |
|
| ThereforeMarks a conclusion that follows from preceding statements. | \therefore |
U+2234 |
|
| Because SymbolIntroduces a reason, premise, or justification in a compact mathematical argument. | \because |
U+2235 |
|
| TurnstileIndicates syntactic derivability from assumptions. | \vdash |
U+22A2 |
|
| ModelsIndicates semantic satisfaction or entailment. | \models |
U+22A8 |
|
| BottomRepresents falsehood in logic or perpendicularity in some contexts. | \bot |
U+22A5 |
|
| Clockwise Circle ArrowRepresents the clockwise circle arrow in mappings, implications, transformations, limits, or paired processes. | \circlearrowright |
U+21BB |
|
| Contains As MemberReverses the element-of relation and says that the set contains the object. | \ni |
U+220B |
|
| Contains with Long Horizontal StrokeThe Unicode character ⋺ is named contains with long horizontal stroke and is used as a specialized mathematical sign in contexts where its exact shape carries meaning. | ⋺ |
U+22FA |
|
| Contains with OverbarThe Unicode character ⋽ is named contains with overbar and is used as a specialized mathematical sign in contexts where its exact shape carries meaning. | ⋽ |
U+22FD |
|
| Contains with Vertical Bar At End Of Horizontal StrokeThe Unicode character ⋻ is named contains with vertical bar at end of horizontal stroke and is used as a specialized mathematical sign in contexts where its exact shape carries meaning. | ⋻ |
U+22FB |
|
| Counterclockwise Circle ArrowRepresents the counterclockwise circle arrow in mappings, implications, transformations, limits, or paired processes. | \circlearrowleft |
U+21BA |
|
| Curly Logical AndRepresents a specialized meet or conjunction operation. | \curlywedge |
U+22CF |
|
| Curly Logical OrRepresents a specialized join or disjunction operation. | \curlyvee |
U+22CE |
|
| Does Not Contain As MemberStates that a set does not contain a given element. | \not\ni |
U+220C |
|
| Does Not Force SymbolStates that a forcing or strong semantic consequence relation does not hold. | \nVdash |
U+22AB |
|
| Does Not Precede Or EqualThe Unicode character ⋠ is named does not precede or equal and is used as a specialized mathematical sign in contexts where its exact shape carries meaning. | ⋠ |
U+22E0 |
|
| Does Not Succeed Or EqualThe Unicode character ⋡ is named does not succeed or equal and is used as a specialized mathematical sign in contexts where its exact shape carries meaning. | ⋡ |
U+22E1 |
|
| Double IntersectionRepresents the double intersection, a specialized mathematical operator or relation whose exact definition depends on context. | \Cap |
U+22D2 |
Verification note
Logic and set notation can change with local convention. Define strict versus non-strict inclusion and operator precedence when ambiguity is possible.
Open the linked full reference for aliases, usage examples, common mistakes, platform input instructions, and related tools.
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