| symbol | latex code | explanation | |
|---|---|---|---|
¬ | \neg | Logical NOT | |
∧ | \land | Logical AND | |
∨ | \lor | Logical OR | |
⊕ | \oplus | Logical XOR | |
→ | \to | Implication (if...then...) | |
↔ | \leftrightarrow | Biconditional (logical equivalence) | |
⊨ | \models | Entails (satisfiability or semantic entailment) | |
⊢ | \vdash | Provable (syntactic entailment) | |
⊤ | \top | Tautology (always true) | |
⊥ | \bot | Contradiction (always false) | |
∀ | \forall | Universal quantifier (for all) | |
∃ | \exists | Existential quantifier (there exists) | |
∄ | \nexists | Negated existential quantifier (there does not exist) | |
∈ | \in | Element of | |
∉ | \notin | Not an element of | |
⊆ | \subseteq | Subset or equal | |
⊂ | \subset | Proper subset | |
⊇ | \supseteq | Superset or equal | |
⊃ | \supset | Proper superset | |
∩ | \cap | Intersection (common elements) | |
∪ | \cup | Union (all elements) | |
∖ | \setminus | Set difference | |
⊆ | \subseteq | Subset or equal (includes equality) | |
⊇ | \supseteq | Superset or equal (includes equality) | |
⊄ | \not\subset | Not subset | |
⊅ | \not\supset | Not superset | |
ℵ₀ | \aleph_0 | Aleph-null (smallest infinite cardinal) | |
𝒫(A) | \mathcal{P}(A) | Power set (set of all subsets) | |
= | = | Equality | |
≠ | \neq | Not equal | |
< | < | Less than | |
> | > | Greater than | |
≤ | \leq | Less than or equal to | |
≥ | \geq | Greater than or equal to | |
∅ | \emptyset | Empty set (no elements) | |
ℕ | \mathbb{N} | Set of natural numbers | |
ℤ | \mathbb{Z} | Set of integers | |
ℚ | \mathbb{Q} | Set of rational numbers | |
ℝ | \mathbb{R} | Set of real numbers | |
ℂ | \mathbb{C} | Set of complex numbers | |
□ | \Box | Necessity (it is necessary that) | |
◇ | \Diamond | Possibility (it is possible that) | |
◊ | \lozenge | Eventually (temporal logic) | |
○ | \bigcirc | Next (temporal logic) | |
⊢ | \vdash | Provable in proof system | |
⊬ | \nvdash | Not provable in proof system | |
⊨ | \models | Semantic entailment | |
⊭ | \nvDash | Not semantic entailment | |
⊣ | \dashv | Assertion of incompatibility | |
∧ | \wedge | Meet (lattice intersection) | |
∨ | \vee | Join (lattice union) | |
⊥ | \bot | Bottom (least element) | |
⊤ | \top | Top (greatest element) | |
Pr(A) | \Pr(A) | Probability of event A | |
E[X] | \mathbb{E}[X] | Expected value of random variable X | |
⇒ | \Rightarrow | Implies in proofs | |
⇐ | \Leftarrow | Implied by in proofs | |
○ | \circ | Composition of functions | |
∞ | \infty | Infinity | |
∴ | \therefore | Therefore (consequence) | |
∵ | \because | Because (reasoning) | |
λ | \lambda | Function abstraction in lambda calculus | |
⊢α | \vdash_\alpha | Type derivability in a type system | |
∼ | \sim | Beta equivalence in lambda calculus | |
≡ | \equiv | Alpha equivalence in lambda calculus | |
Γ | \Gamma | Context or typing environment in type systems |