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Logic Symbols
Explore our complete math symbols list and interactive keyboard to lookup meanings, LaTeX codes, and UTF-8 characters for logic symbols. Propositional and predicate logic operators such as AND, OR, NOT, implication, quantifiers, and equivalence.
Logic Symbols Reference Table
| Action | Symbol | Name | Meaning | Example | LaTeX | Unicode |
|---|---|---|---|---|---|---|
| ∧ | Logical Conjunction (AND) | True if and only if both operands are true. | P ∧ Q is true when P = true and Q = true | \land \text{ or } \wedge | U+2227 | |
| ∨ | Logical Disjunction (OR) | True if at least one operand is true. | P ∨ Q | \lor \text{ or } \vee | U+2228 | |
| ¬ | Logical Negation (NOT) | Inverts the truth value of a proposition. | ¬(true) = false | \neg \text{ or } \lnot | U+00AC | |
| ⇒ | Material Implication (If-Then) | Asserts that if premise P is true, then conclusion Q must be true. | x = 2 ⇒ x² = 4 | \implies \text{ or } \Rightarrow | U+21D2 | |
| ⇔ | Logical Equivalence (If and Only If) | Bi-conditional: P and Q always share identical truth values. | x + 1 = 3 ⇔ x = 2 | \iff \text{ or } \Leftrightarrow | U+21D4 | |
| ∀ | Universal Quantifier (For All) | Indicates that the predicate statement holds for all members of a domain. | ∀ x ∈ ℝ, x² ≥ 0 | \forall | U+2200 | |
| ∃ | Existential Quantifier (There Exists) | States that there is at least one element in the domain satisfying the statement. | ∃ x ∈ ℝ, x² = 2 | \exists | U+2203 | |
| ∄ | There Does Not Exist | No member of the specified domain satisfies the given condition. | ∄ x ∈ ℝ, x² = −1 | \nexists | U+2204 | |
| ∴ | Therefore | Used before a logical conclusion derived from preceding premises. | All humans are mortal. Socrates is human. ∴ Socrates is mortal. | \therefore | U+2234 | |
| ∵ | Because / Since | Introduces a reason or justification for a stated mathematical deduction. | x² = 4 ⟹ x = ±2 ∵ 2² = (−2)² = 4 | \because | U+2235 | |
| ⊢ | Turnstile (Proves / Entails) | Syntactic deduction: conclusion can be formally proved from assumptions. | A, A → B ⊢ B | \vdash | U+22A2 | |
| ⊨ | Double Turnstile (Models / Semantic Entailment) | Semantic entailment: whenever premises are true, conclusion is guaranteed true. | Γ ⊨ φ | \vDash | U+22A8 | |
| ⊭ | Does Not Entail | Indicates that A does not semantically entail proposition B. | A ⊭ B | \nvDash | U+22AD | |
| ⊬ | Does Not Prove | Indicates that B cannot be derived from A in this system. | T ⊬ G | \nvdash | U+22AC |