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**Table of Content**

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.

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.

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.

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 (|)

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.

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

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

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

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.

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.