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Relations and Functions Calculator

Online mapping checker: decide whether a finite correspondence is a function, injective, surjective, or bijective.

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Injective: distinct y; surjective: covers codomain; bijective: both
Domain
Paired with X
Codomain

📖 Tutorial | Mappings

1. Definition
A function maps each domain element uniquely; injective gives distinct y, surjective covers the codomain, bijective is both.
2. Formula & Notation
Injective, surjectiveDistinct, covering
3. Properties & Laws
  • Unique image;
  • Injective;
  • Surjective;
  • Bijective is invertible.
4. Steps
  1. Enter X, Y (paired), codomain C;
  2. Click "Check";
  3. Or click "Load Example".
5. Worked Examples
Example: 1,2,3→2,4,6, codomain has 8: function, injective, not surjective.
6. Common Pitfalls
X and Y counts match;
Injection via y;
Surjection via codomain.

❓ FAQ | Mappings

Mapping?
Unique image.
Injective?
Distinct y.
Surjective?
Covers codomain.
Bijective?
Both.
Example?
Injective.
Repeated domain?
Not a function.