= Complete Relation Symbols Generator
Master mathematical relations, logical operators, and set relations with =, ≠, ≈, ≅, ∈, ⊂, →, ⊢ symbols. Perfect for mathematics, computer science, and logic with interactive relation calculator.
🧮 Relation Calculator
Evaluate relation expressions, check mathematical relationships, and work with logical and set theory relations with step-by-step solutions.
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Complete Mathematical Relations & Symbols
⚖️ Equality & Equivalence Relations
EQUALS
NOT EQUAL
APPROXIMATELY EQUAL
CONGRUENT
IDENTICALLY EQUAL
NOT IDENTICAL
SIMILAR
ASYMPTOTICALLY EQUAL
EQUIVALENT TO
ALL EQUAL TO
EQUALS BY DEFINITION
MEASURED BY
QUESTIONED EQUAL
PROPORTIONAL TO
APPROACHES LIMIT
GEOMETRICALLY EQUAL
📊 Comparison & Order Relations
LESS THAN
LESS EQUAL
GREATER EQUAL
MUCH LESS
MUCH GREATER
NOT LESS
NOT GREATER
NEITHER LESS NOR EQUAL
NEITHER GREATER NOR EQUAL
VERY MUCH LESS
VERY MUCH GREATER
LESS OR GREATER
GREATER OR LESS
NEITHER LESS NOR GREATER
NEITHER GREATER NOR LESS
🧠 Logical & Modal Relations
IMPLIES
BICONDITIONAL
DOUBLE ARROW IMPLIES
DOUBLE ARROW BICONDITIONAL
ENTAILES
SEMANTICALLY ENTAILS
DOES NOT ENTAIL
MODELS
DOES NOT PROVE
TURNSTYLE
DOES NOT ENTAIL
ASSERTION
NECESSARILY
POSSIBLY
LEFT ARROW IMPLIES
LEFT DOUBLE ARROW
∈ Set Theory Relations
ELEMENT OF
NOT ELEMENT OF
CONTAINS AS MEMBER
DOES NOT CONTAIN
SUBSET
SUBSET EQUAL
SUPERSET
SUPERSET EQUAL
NOT SUBSET
NEITHER SUBSET NOR EQUAL
NOT SUPERSET
NEITHER SUPERSET NOR EQUAL
EMPTY SET
UNION
INTERSECTION
SET DIFFERENCE
SYMMETRIC DIFFERENCE
🔄 Equivalence & Similarity Relations
TILDE
ASYMPTOTICALLY EQUAL
EQUIVALENT TO
ALL EQUAL TO
EQUALS BY DEFINITION
MEASURED BY
QUESTIONED EQUAL
PROPORTIONAL TO
APPROACHES LIMIT
GEOMETRICALLY EQUAL
APPROXIMATELY EQUAL
IMAGE OF
COLON EQUALS
EQUALS COLON
📝 Specialized Relations & Symbols
SQUARE IMAGE OF
SQUARE ORIGINAL OF
SQUARE IMAGE OR EQUAL
SQUARE ORIGINAL OR EQUAL
THEREFORE
BECAUSE
ASSERTION
DOES NOT PROVE
TRUE
NOT TRUE
FORCES
TRIPLE TURNSTYLE
DOUBLE TURNSTYLE
NOT FORCES
PRECEDES UNDER RELATION
SUCCEEDS UNDER RELATION
Mathematical Relation Expressions & Examples
a = b
Table of Contents
🔗 Complete Relation Symbols Reference Table
Master the complete collection of mathematical relations, logical operators, and set theory symbols with our comprehensive reference table. Click any symbol to copy it instantly for use in your mathematical proofs, computer programs, and research papers.
| Symbol | Name | HTML Code | Unicode | Category | Usage |
|---|---|---|---|---|---|
| ⚖️ Equality Relations | |||||
| = | Equals | = | U+003D | Equality | a = b |
| ≠ | Not Equal | ≠ | U+2260 | Inequality | a ≠ b |
| ≈ | Approximately Equal | ≈ | U+2248 | Approximation | a ≈ b |
| ≅ | Congruent | ≅ | U+2245 | Congruence | a ≅ b |
| ≡ | Identically Equal | ≡ | U+2261 | Identity | a ≡ b |
| 📊 Comparison Relations | |||||
| < | Less Than | < | U+003C | Comparison | a < b |
| > | Greater Than | > | U+003E | Comparison | a > b |
| ≤ | Less Than or Equal | ≤ | U+2264 | Comparison | a ≤ b |
| ≥ | Greater Than or Equal | ≥ | U+2265 | Comparison | a ≥ b |
| ≪ | Much Less Than | ≪ | U+226A | Comparison | a ≪ b |
| 🧠 Logical Relations | |||||
| → | Implies | → | U+2192 | Implication | P → Q |
| ↔ | If and Only If | ↔ | U+2194 | Biconditional | P ↔ Q |
| ⊢ | Entails | ⊢ | U+22A2 | Entailment | Γ ⊢ φ |
| ⊨ | Semantically Entails | ⊨ | U+22A8 | Semantic Entailment | Γ ⊨ φ |
| ∈ Set Relations | |||||
| ∈ | Element of | ∈ | U+2208 | Membership | x ∈ A |
| ⊂ | Subset | ⊂ | U+2282 | Containment | A ⊂ B |
| ⊆ | Subset or Equal | ⊆ | U+2286 | Containment | A ⊆ B |
| ⊃ | Superset | ⊃ | U+2283 | Containment | A ⊃ B |
| ⊇ | Superset or Equal | ⊇ | U+2287 | Containment | A ⊇ B |
💡 Quick Relation Symbol Reference
Basic Relations
= Equals • ≠ Not Equal • ≈ Approximately • < Less • > Greater
Logical Relations
→ Implies • ↔ Bicon • ⊢ Entails • ⊨ Sem Entails • ∀ For All
Set Relations
∈ Element • ⊂ Subset • ∪ Union • ∩ Intersection • ∅ Empty
Special Relations
∴ Therefore • ∵ Because • ∝ Proportional • ∼ Similar • ≅ Congruent
Mathematical Relations, Logic and Applications
a = b
Basic equality relation – a equals b
Basic equality relation – a equals b
x ∈ ℝ ∧ y ∈ ℝ → x + y ∈ ℝ
Set membership with logical implication – if x and y are real numbers, their sum is also real
Set membership with logical implication – if x and y are real numbers, their sum is also real
∀x(P(x) → Q(x))
Universal quantification with implication – for all x, if P(x) then Q(x)
Universal quantification with implication – for all x, if P(x) then Q(x)
A ⊂ B ∧ B ⊂ C → A ⊂ C
Set containment transitivity – subset relation is transitive
Set containment transitivity – subset relation is transitive
Γ ⊨ φ
Semantic entailment – Γ semantically entails φ
Semantic entailment – Γ semantically entails φ
lim x→∞ f(x) = L
Limit definition using equality and arrow – the limit as x approaches infinity
Limit definition using equality and arrow – the limit as x approaches infinity
∃x ∀y R(x,y)
Existential-universal quantification – there exists x such that for all y, R(x,y) holds
Existential-universal quantification – there exists x such that for all y, R(x,y) holds
a ≪ b ≪ c
Chained much-less-than relations – a is much less than b, which is much less than c
Chained much-less-than relations – a is much less than b, which is much less than c
f(x) ≃ g(x) as x → ∞
Asymptotic equivalence – functions f and g are asymptotically equivalent
Asymptotic equivalence – functions f and g are asymptotically equivalent
A ≅ B ≝ A is isomorphic to B
Congruence definition – A is congruent to B, defined as isomorphic
Congruence definition – A is congruent to B, defined as isomorphic
P ⊨ Q ∴ ¬P ∨ Q
Semantic entailment with therefore – P entails Q, therefore not P or Q
Semantic entailment with therefore – P entails Q, therefore not P or Q
∅ ⊂ A ∧ A ⊆ ℝ
Empty set subset and real numbers containment – empty set is subset of A, A is subset of reals
Empty set subset and real numbers containment – empty set is subset of A, A is subset of reals