Logic
Truth table builder
Use variables like p, q, r with !, &&, ||, ->, <->, xor, parentheses.
| p | q | result |
|---|---|---|
| F | F | T |
| F | T | T |
| T | F | T |
| T | T | T |
Tautology
Discrete math, taught interactively
Discretica
Interactive discrete math for CS students: topics, proof trainer, practice, and browser-native tools.
7topics
534problems
54formulas
60proof tasks
Calculators
Discrete math tools
All calculations run in the browser with validated inputs and shareable route URLs.
Sets
Set operations
A = {1, 2, 3, 5}
B = {2, 4, 5, 8}
A union B = {1, 2, 3, 5, 4, 8}
A intersection B = {2, 5}
A - B = {1, 3}
B - A = {4, 8}
Symmetric difference = {1, 3, 4, 8}Number theory
GCD / LCM
numbers: 84, 126, 210 gcd: 42 lcm: 1260
Representation
Base converter
255 base 10 = 255 base 10 255 base 10 = FF base 16
Counting
Combinatorics
n! = 3628800 P(n,r) = n! / (n-r)! = 720 C(n,r) = n! / (r!(n-r)!) = 120
Modular arithmetic
Modulo calculator
(17 ^ 5) mod 7 = 5
Source tools
7 mobile tool definitions
Truth Table BuilderGenerate truth tables for any logical proposition
Set OperationsPerform set operations with visual Venn diagrams
Combinatorics CalculatorCalculate permutations, combinations, and more
Modular ArithmeticPerform modular arithmetic operations step by step
Base ConverterConvert numbers between binary, octal, decimal, and hex
GCD & LCM CalculatorFind GCD and LCM using the Euclidean algorithm
Proof TrainerPractice building proofs step by step
Formula references
Quick lookup
De Morgan's Law (AND)
¬(p ∧ q) ≡ ¬p ∨ ¬qDe Morgan's Law (OR)
¬(p ∨ q) ≡ ¬p ∧ ¬qConditional Equivalence
p → q ≡ ¬p ∨ qContrapositive
p → q ≡ ¬q → ¬pBiconditional Expansion
p ↔ q ≡ (p → q) ∧ (q → p)Distributive Law (AND over OR)
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)Distributive Law (OR over AND)
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)Absorption Law (1)
p ∨ (p ∧ q) ≡ pDirect Proof Structure
Assume P. Derive Q. Therefore P → Q.Proof by Contrapositive
Prove ¬Q → ¬P instead of P → Q