1. Truth tables & classification
Type a propositional formula in variables p q r s. Operators: ~ & | -> <-> ^ (not, and, or, implies, iff, xor). The table is built row by row and the formula is classed as tautology, contradiction or contingency.
2. Predicates & quantifiers
A domain of integers and a predicate $P(x)$. See where $\forall x\,P(x)$ and $\exists x\,P(x)$ hold, and how negation flips the quantifier: $\neg\forall x\,P(x)\equiv\exists x\,\neg P(x)$.
3. Set algebra — three-set Venn
Click regions to toggle them into your set. The matching expression in $A,B,C$ and the cardinality update live. Universe is the 1..30 integers split across the three circles.
Regions are the 7 disjoint pieces of the Venn diagram plus the outside.
4. Functions — injective, surjective, bijective
Each domain element maps to one codomain element. Click a domain node, then a codomain node to rewire it. The classification updates from the current mapping.
5. Relations — properties & closures
Toggle cells of the relation matrix on $\{1..n\}$. Properties are checked live. Show the reflexive / symmetric / transitive closure as faint added cells.
6. Graphs — Euler & Hamilton paths
Click empty space to add a vertex; click two vertices to toggle an edge. Degrees, connectivity and the existence of Euler / Hamilton paths are detected live.
7. Modular arithmetic
A clock with $n$ positions. Step by $+a$ to walk the residues, read the operation tables, and run the Euclidean algorithm for $\gcd$.
8. Integer representation
A value shown as bits. Read it in binary, octal and hex, and toggle two's-complement to see how negatives are encoded in a fixed width.
9. Finite-state machine
A deterministic automaton over the alphabet $\{0,1\}$. Type an input string and step through it; the current state is highlighted and the string is accepted iff it ends in a final state.