Calculators
Interactive discrete math for CS students: topics, proof trainer, practice, and browser-native tools.
What is in here
Calculators
Six calculators that run entirely in this browser. Inputs are validated, so a rejected entry says what is wrong instead of returning a confident wrong answer.
Logic
Enumerate every assignment of a proposition and classify it as a tautology, a contradiction, or a contingency.
Variables like p, q, r with ! && || -> <-> xor and parentheses. Words work too: not, and, or, iff. Up to 6 variables.
| p | q | result |
|---|---|---|
| F | F | T |
| F | T | T |
| T | F | T |
| T | T | T |
Sets
Union, intersection, both differences, and the symmetric difference of two sets.
Separate elements with commas or spaces. Duplicates collapse, because a set holds each element once. Leaving one side blank is a real question - that side is the empty set.
Number theory
Greatest common divisor and least common multiple, computed exactly - the LCM is arbitrary-precision, so large coprime inputs stay correct.
Commas or spaces, up to 12 values. Anything that is not a whole number is named back rather than coerced.
Representation
Rewrite an integer in any base from 2 to 36, with the decimal value shown alongside.
Digits run 0-9 then a-z. A leading minus sign is kept.
Counting
Permutations and combinations of r items drawn from n, in exact arbitrary-precision arithmetic.
Whole numbers with 0 ≤ r ≤ n ≤ 200. Blank fields and exponent notation are refused, not read as zero.
Modular arithmetic
Arithmetic in ℤ/mℤ, including fast modular exponentiation and the modular inverse.
Results are the least non-negative residue. Exponents must be zero or greater.
Source tools
Formula references
¬(p ∧ q) ≡ ¬p ∨ ¬q¬(p ∨ q) ≡ ¬p ∧ ¬qp → q ≡ ¬p ∨ qp → q ≡ ¬q → ¬pp ↔ q ≡ (p → q) ∧ (q → p)p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)p ∨ (p ∧ q) ≡ pAssume P. Derive Q. Therefore P → Q.Prove ¬Q → ¬P instead of P → Q