Truth Table Generator

Available Operators:

  • AND or && : Logical AND
  • OR or || : Logical OR
  • NOT or ! : Logical NOT
  • XOR : Exclusive OR
  • IMPLIES or -> : Implication
  • () : Grouping

Understanding Truth Tables

What are Truth Tables?

Truth tables are fundamental tools in logic that show all possible combinations of inputs and their corresponding outputs for logical expressions.

Basic Operations:

  • AND (∧): True only if both inputs are true
  • OR (∨): True if at least one input is true
  • NOT (¬): Inverts the input
  • XOR (⊕): True if inputs are different
  • IMPLIES (→): False only if antecedent true and consequent false

Applications and Uses

  • Digital Circuit Design
    • Logic Gate Implementation
    • Circuit Minimization
    • State Machine Design
  • Computer Science
    • Boolean Algebra
    • Program Logic
    • Database Queries
  • Mathematics
    • Propositional Logic
    • Set Theory
    • Mathematical Proofs
  • Artificial Intelligence
    • Expert Systems
    • Decision Trees
    • Logic Programming

Advanced Concepts

Tautologies

Always true expressions

Contradictions

Always false expressions

Contingencies

Sometimes true/false

Normal Forms

CNF and DNF representations

Karnaugh Maps

Visual minimization

Logical Equivalence

Same truth values