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.

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.

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.

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

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

Two-Set Venn Diagram Basic Identities Explorer

Shade the Venn diagram for any two-set identity — union, intersection, complement, the three differences, De Morgan

Key Terms

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.

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.

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.