🧠 Complete Logic Symbols Generator
Master logic with ∧, ∨, ¬, →, ↔, ∀, ∃, ⊢, ⊨, mathematical logic and propositional calculus. Perfect for logic students, philosophers, computer scientists, and mathematicians with interactive truth table builder.
🧮 Logic Calculator
Evaluate logical expressions, build truth tables, and perform logical operations with step-by-step solutions.
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Complete Logical Symbols & Operators
∧ Logical Operators & Connectives
AND
OR
NOT
IMPLIES
BICONDITIONAL
EQUIVALENCE
XOR
XOR
∀ Quantifiers
FOR ALL
THERE EXISTS
DOES NOT EXIST
FOR ALL x
THERE EXISTS x
FOR ALL y
THERE EXISTS y
FOR ALL z
□ Modal Logic
NECESSARILY
POSSIBLY
DIAMOND
NECESSARILY P
POSSIBLY P
NOT NECESSARILY
NOT POSSIBLY
STRICT IMPLICATION
STRICT EQUIVALENCE
⊢ Proof Theory & Relations
ENTAILES
SEMANTICALLY ENTAILS
DOES NOT ENTAIL
MODELS
DOES NOT PROVE
TURNSTYLE
DOES NOT ENTAIL
ASSERTION
∈ Set Theory
ELEMENT OF
NOT ELEMENT OF
SUBSET
SUBSET OR EQUAL
SUPERSET
SUPERSET OR EQUAL
EMPTY SET
UNION
INTERSECTION
SET DIFFERENCE
SYMMETRIC DIFFERENCE
⊕ Boolean Logic
XOR
XOR
NAND
NOR
NAND
NOR
XNOR
XNOR
BUFFER
NOT BUFFER
📝 Additional Logic Symbols
THEREFORE
BECAUSE
QED
UNIQUE EXISTENTIAL
MATERIAL IMPLICATION
MATERIAL EQUIVALENCE
Logical Expressions & Examples
P ∧ Q → R
Table of Contents
🧠 Complete Logic Symbols Reference Table
Master the complete collection of logic symbols with our comprehensive reference table. Click any symbol to copy it instantly for use in your logical proofs, computer science papers, and mathematical research.
| Symbol | Name | HTML Code | Unicode | Category | Usage |
|---|---|---|---|---|---|
| 🔗 Logical Operators & Connectives | |||||
| ∧ | Logical AND | ∧ | U+2227 | Binary Operator | P ∧ Q |
| ∨ | Logical OR | ∨ | U+2228 | Binary Operator | P ∨ Q |
| ¬ | Logical NOT | ¬ | U+00AC | Unary Operator | ¬P |
| → | Logical IMPLIES | → | U+2192 | Binary Operator | P → Q |
| ↔ | Logical BICONDITIONAL | ↔ | U+2194 | Binary Operator | P ↔ Q |
| ⊕ | Exclusive OR (XOR) | ⊕ | U+2295 | Binary Operator | P ⊕ Q |
| ⊼ | NAND | ⌅ | U+22BC | Binary Operator | P ⊼ Q |
| ⊽ | NOR | ⊻ | U+22BD | Binary Operator | P ⊽ Q |
| ∀ Quantifiers | |||||
| ∀ | Universal Quantifier | ∀ | U+2200 | Quantifier | ∀x(P(x)) |
| ∃ | Existential Quantifier | ∃ | U+2203 | Quantifier | ∃x(P(x)) |
| ∃! | Unique Existential | ∃! | U+2203 U+0021 | Quantifier | ∃!x(P(x)) |
| □ Modal Logic | |||||
| □ | Necessarily | &box; | U+25A1 | Modal Operator | □P |
| ◇ | Possibly | ◊ | U+25CA | Modal Operator | ◇P |
| ⊨ | Strict Implication | ⊨ | U+22A8 | Modal Relation | □P ⊨ □Q |
| ≡ | Strict Equivalence | ≡ | U+2261 | Modal Relation | P ≡ Q |
| ⊢ Proof Theory & Relations | |||||
| ⊢ | Entails/Provable | ⊢ | U+22A2 | Meta-relation | Γ ⊢ φ |
| ⊨ | Semantically Entails | ⊨ | U+22A8 | Meta-relation | Γ ⊨ φ |
| ∈ Set Theory | |||||
| ∈ | Element of | ∈ | U+2208 | Set Relation | x ∈ A |
| ⊂ | Subset | ⊂ | U+2282 | Set Relation | A ⊂ B |
| ∪ | Union | ∪ | U+222A | Set Operation | A ∪ B |
| ∩ | Intersection | ∩ | U+2229 | Set Operation | A ∩ B |
| ∖ | Set Difference | ∖ | U+2216 | Set Operation | A ∖ B |
| △ | Symmetric Difference | △ | U+2206 | Set Operation | A △ B |
| 📝 Additional Logic Symbols | |||||
| ∴ | Therefore | ∴ | U+2234 | Logical Symbol | ∴ |
| ∵ | Because | ∵ | U+2235 | Logical Symbol | ∵ |
| ∎ | QED (End of Proof) | ∎ | U+220E | Proof Symbol | ∎ |
| ⊃ | Material Implication | ⊃ | U+2283 | Logical Operator | P ⊃ Q |
| ≡ | Material Equivalence | ≡ | U+2261 | Logical Operator | P ≡ Q |
| ⊦ | Buffer | ⊦ | U+22A6 | Boolean Gate | ⊦ |
| ⊬ | Not Buffer | ⊬ | U+22AC | Boolean Gate | ⊬ |
💡 Quick Logic Symbol Reference
Basic Connectives
∧ AND • ∨ OR • ¬ NOT
Implication
→ IMPLIES • ↔ BICONDITIONAL
Quantifiers
∀ FOR ALL • ∃ THERE EXISTS
Relations
⊢ ENTAILS • ⊨ SEMANTICALLY ENTAILS
Logical Expressions and Applications
P ∧ Q → R
Logical implication – if P and Q then R
Logical implication – if P and Q then R
∀x(P(x) → Q(x))
Universal quantification – for all x, if P(x) then Q(x)
Universal quantification – for all x, if P(x) then Q(x)
⊢ P ∨ ¬P
Law of excluded middle – provable that P or not P
Law of excluded middle – provable that P or not P
∃x∀y(P(x,y))
Existential-universal quantification
Existential-universal quantification
□(P → Q) → (◇P → ◇Q)
Modal logic – necessarily implies modal inference
Modal logic – necessarily implies modal inference
Γ ⊨ φ
Semantic entailment – Γ semantically entails φ
Semantic entailment – Γ semantically entails φ
P ⊕ Q ↔ (P ∧ ¬Q) ∨ (¬P ∧ Q)
Exclusive OR definition
Exclusive OR definition
∀x∃y(P(x) ∧ Q(y,x))
Mixed quantification with relations
Mixed quantification with relations