Set Theory Visual Tools

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Free interactive tools for learning set theory

Shade any region of a Venn diagram and watch a set identity prove itself. Build a set from a domain and a condition and see every candidate tested one at a time. Draw a power set as a subset lattice, step through inclusion-exclusion one term at a time, and read the same expression as both shaded regions and a truth table.

💡Tip: Start with the Two-Set Venn Diagram Basic Identities Explorer to see how each region maps to a set expression.

11Tools

7Categories

100%Free

1 tool

Diagrams

Set Theory Diagrams

A gallery of every diagram already shown on the set theory pages: figures drawn for the lessons and frozen states of the visual tools. Browse by chapter or page, search captions, compare two figures side by side, and jump from any picture to the exact section where it appears or to the tool that drew it.

1 tool · 1 sub-group

Counting and Cardinality

Inclusion-Exclusion1 tool

Inclusion-Exclusion Principle Explorer

Enter the sizes of two or three sets and their overlaps, then apply the inclusion-exclusion formula one term at a time. Each region of the diagram shows how many times it has been counted so far, so the over-counting appears, the subtractions overshoot on the triple overlap, and the final term repairs it. The walk-through ends when every region reads exactly one.

1 tool · 1 sub-group

Sets and Subsets

Power Sets1 tool

Power Set Explorer

Draw the power set of a set of up to five elements as a Hasse diagram of the subset lattice. Click any subset and its subsets light up below it while its supersets light up above it, so containment reads as a direction on the page. A level table counts each size as a binomial coefficient and totals them to 2 to the n, and a roster panel lists every subset in set notation.

1 tool · 1 sub-group

Set Notation

Set-Builder1 tool

Set-Builder Notation Explorer

Assemble a set-builder expression one piece at a time: choose a domain, add conditions such as even, prime or less than, and join them with and or or. Every candidate in the domain appears as a chip that turns green when it passes, clicking one shows it tested condition by condition, and a roster panel prints the finished set — or says why it cannot be listed.

5 tools · 3 sub-groups

Venn Diagrams

Three Sets2 tools

Three-Set Venn Diagram Basic Identities Explorer

Shade the three-circle Venn diagram for any three-set identity — triple union and intersection, complements, the various differences, counting identities like exactly two of A, B, C, and De Morgan's laws for three sets. Switch between six category tabs, pick an identity from the formula buttons or the Jump-to dropdown, and customize the shading color and opacity. Each highlighted region updates with an explanation panel showing the set-builder notation.

Three-Set Venn Diagram Laws and Complex Identities Explorer

Verify three-set algebraic laws by shading both sides of each identity on a pair of side-by-side three-circle Venn diagrams. Browse 12 laws across four categories — associative laws for union, intersection, and symmetric difference; distributive laws; three-set De Morgan's laws; and five difference identities — and watch the match indicator confirm each visual proof across all eight regions.

Two Sets2 tools

Two-Set Venn Diagram Basic Identities Explorer

Shade the Venn diagram for any two-set identity — union, intersection, complement, the three differences, De Morgan's laws, and set relations like subset and disjoint. Switch between categories using the tabs, pick an identity from the formula buttons or Jump-to dropdown, and customize the shading color and opacity. Each highlighted region updates with an explanation panel showing the set-builder notation.

Two-Set Venn Diagram Laws and Identities Explorer

Verify two-set algebraic laws by shading both sides of each identity on a pair of side-by-side Venn diagrams. Browse 27 laws across eight categories — idempotent, commutative, identity, complement, De Morgan's, absorption, difference, and compound complements — and watch the match indicator confirm each visual proof.

Multiple Sets1 tool

Venn Diagram Generator

Shade any set expression on a 2, 3, 4, or 5 set Venn diagram. Type it with keyboard shortcuts, build it from symbol buttons, or load a preset. A region strip lists every region and whether it is shaded, a compare box tests two expressions for equivalence, and finished diagrams export to SVG or PNG.

1 tool · 1 sub-group

Set Operations

Indexed Families1 tool

Indexed Union and Intersection Explorer

Pick a family of sets indexed by 1, 2, 3 and upward, then raise the index and watch the big union and the big intersection accumulate in opposite directions. Interval families are drawn on a shared number line with endpoint marks that matter, discrete families as a membership grid, and the finite families on a Venn diagram. Each family is built to make one limit surprising.

1 tool · 1 sub-group

Logic and Sets

Truth Tables1 tool

Venn Diagram and Truth Table Explorer

One set expression shown two ways at once — as shaded regions of a two or three set Venn diagram, and as a truth table with a result column. Clicking a row outlines the region it describes, and clicking a region selects its row. The tool also rewrites every expression into logical notation and flags tautologies, contradictions, and expressions that ignore one of their sets.