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Set Theory Explorer

// CARTESIAN PRODUCT · RELATIONS · FUNCTIONS · DOMAIN & RANGE

Define Your Sets

Set A (x-axis)

Set B (y-axis)

|A|

|B|

|A×B|

Cartesian Product A × B

          Enter Cartesian product pairs first. Relation R must be a subset.

          Required format: (1,2),(2,4) — comma-separated pairs only. Ctrl+Enter to add.

A×B = ∅

Define sets to see A×B.

Set of Relations R

R = ∅

Define sets to see R.

Choose a Relation Rule

Grid

A × B — Cartesian Product visualised

scroll / pinch / drag to zoom & pan · tap a point for its coordinates

A×B point

R pair (relation)

Codomain + Range (y-axis)

Identity

Universal

Reflexive

Symmetric

Transitive

Equivalence ★

Partial Order ★

Relation Properties

Define sets to detect types.

Inverse & Composition

Define sets to compute R⁻¹ and R∘R.

Domain & Range Map — after rule

            Fills in once a relation rule is applied — shows domain/range filtered by R
          

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🟢 Domain A

Range B

R pair (after rule)

40px/u

Function Types

Relation Info

Define sets and choose a rule to see relation details.

Colour Key

⬡ Scale Views

🟢 Domain A

Codomain B

A×B pair (full product) R relation (REL toggle) Domain of R (⊆ Set A)

40px/u · scroll/pinch zoom · drag pan