p | q | p→q |
---|---|---|

F | F | V |

F | V | V |

V | F | F |

V | V | V |

x

- Input field
- Buttons to move the cursor
- AC allows you to delete everything, while DEL deletes the character to the left of the cursor
- Parentheses
- Negation (~), Conjunction (∧), Disjunction (∨), Conditional (→), Biconditional (↔), Exclusive disjunction (⊕)
- Propositional variables (p,q,r,s), you can use as many variables as you need using the keyboard of your device.
- Button to generate the truth table

The online Truth Table Generator that we put in your hands here is a powerful tool capable of operating with highly complex propositional logic statements. It can process multiple logical statements at the same time, providing the ability to work with a nearly infinite variety of logical statements. Whether you’re a student just beginning to explore propositional logic, an educator looking for teaching resources, or a professional who needs to create truth tables as part of a larger project, our Truth Table Generator is the solution you need.

The Truth Table Generator has a simple and intuitive interface that makes its use much easier. To use it you will only have to enter the logical statement in the input field, either using the virtual keyboard of the generator itself or that of your device, and press the “=” button on the virtual keyboard to obtain the resulting truth table.

To build your logical sentences you have the following propositions on the virtual keyboard:

**p, q, r, s**

But you can enter as many variables as you need using your device’s keyboard.

If you press the button with a question mark located in the upper left, a box will be displayed explaining the function of part of the truth table generator.

The Truth Table is a graphical procedure that allows determining the possible truth values of a compound proposition, based on the combinations of the truth values of the simple propositions that compose them.

The negation operator, commonly represented by the tilde (~) or by the symbol ¬, negates or changes the truth value of a proposition or sentence.

The conjunction operator, also known as the AND operator and commonly represented with the symbol ∧, is a binary operator that requires both propositions on which it acts to be true to produce a true value. All other cases result in a false value.

p∧q truth table

The disjunction operator, also known as the OR operator and represented with the symbol ∨, returns a true value if at least one of the propositions on which it operates has a true value.

p v q truth table

The XOR operator, also known as exclusive OR and represented by the symbol ⊕, generates a true value if the two propositions have different values.

p⊕q truth table

Also known as a conditional operator and represented by the symbol → , it returns a value true in all cases except the case T → F. Since this can be a bit difficult to remember, it may be useful to note that this is logically equivalent to ~ p ∨ q as shown in the following tables.

This operator, commonly represented with the symbol ↔, is the conjunction (p → q) ∧ (q → p). This operator is also known as logical equivalence because it only presents a true value if both propositions are equal.

To build truth tables you only have to follow a few very simple and clear steps. Next we will explain each of the steps necessary to make a truth table, using the statement (p→q)∧r as an example:

- Determines the number of rows in the truth table. For this you only have to raise 2 to the number of propositions present in the sentence.

2^{n}

For example, in the case of the statement (p→q)^r, 8 rows must be created.

- Create a column for each proposition.

- Enter all possible combinations of truth values in this part of the table.

- We add to the right a column for each compound proposition and the complete sentence, arranging them from left to right according to the order of dependency.

- And finally we calculate the truth values for each of the compound propositions from left to right.