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Truth Table Calculator

Truth Table Calculator

Write down a logical formula and the calculator will instantly compute truth table values for it, with the steps shown.

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Enter an Equation

Symbols
Negation ~
Conjunction (AND) &
Disjunction (OR) v
Conditional ->
Biconditional <->
Sheffer Stroke |
Absurdity #
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Table of Content

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This truth table calculator will provide the truth table values for the given propositional logic formulas. The propositional logic statements can only be true or false.

What is Truth Table?

The truth table is a tabular view of all combinations of values for the inputs and their corresponding outputs. It is a mathematical table that shows all possible results that may be occur from all possible scenarios. It is used for logic tasks such as logic algebra and electronic circuits.

Prepositional Truth Tables Logic

A proposition is a set of declarative statements with a truth value of “true” or a truth value of “false”. Propositional expressions are composed of connectives and propositional variables. We use capital letters to represent the propositional variables (A, B). The connectives connect the propositional variables.

How to Make a Truth Table?

Connectives:

In propositional logic truth table calculator uses the different connectives which are −

  • OR (∨)
  • AND (∧)
  • Negation/ NOT (¬)
  • Implication / if-then (→)
  • If and only if (⇔)
  • Absurdity (#)
  • Sheffer Stroke (|)

Propositional Equivalences

Two statements A and B are logically equivalent if any of the following two conditions hold –

  • The bi-conditional statement A⇔B is a tautology.
  • The truth tables of every statement have the same truth variables.

Example:

Prove ~(P ∨ Q) and [(~P) ∧ (~Q)] are equivalent

Solution:

The truth tables calculator perform testing by matching truth table method

P Q P ∨ Q ¬ (P ∨ Q) ¬ P ¬ Q [(¬ P) ∧ (¬ Q)]
T T T F F F F
T F T F F T F
F T T F T F F
F F F T T T T

Here, we can see the truth values of ~(P ∨ Q) and [(~P) ∧ (~Q)] are same, hence all the statements are equivalent.

How does Truth Table Calculator Works?

An online truth table generator provides the detailed truth table by following steps:

Input:

  • First, enter a propositional logic equation with symbols.
  • Hit the calculate button for results.

Output:

  • Our calculator construct a truth table for 4 variables of the given expression.

Conclusion

Use this online truth table generator to create the multivariate propositional logic truth tables. Propositional logic deals with statements that can be truth values, “true” and “false”. The purpose is to analyze these statements individually or collectively.

Reference:

From the source of Wikipedia: Unary operations, Logical true, Logical false, Logical identity, Logical negation, Binary operations, Logical conjunction (AND), Logical disjunction (OR), Logical implication.