Logic Proof Calculator

Reviewed by David Chen, PhD in Mathematical Logic | Last Updated: October 2023

Use this Logic Proof Calculator to determine the validity of logical statements. Enter your truth values and operators to instantly generate the logical proof result and see the step-by-step truth table evaluation.

Logic Proof Calculator

Represents the first premise or variable.

The logical relationship between P and Q.

Represents the second premise or variable.

Logic Proof Calculator Formula

In propositional logic, the validity of an argument is determined by its form. This calculator uses standard truth table definitions to solve logical proofs.

Result = P [Operator] Q

Depending on the operator selected, the logic follows standard boolean algebra rules. For more formal definitions, refer to the Stanford Encyclopedia of Philosophy.

Variables

• P (Proposition 1): The first logical statement or antecedent. It can be either True or False.
• Q (Proposition 2): The second logical statement or consequent. It can be either True or False.
• Operator: The logical connective (AND, OR, IMPLIES, etc.) that binds the variables together.

Related Calculators

• Truth Table Generator
• Boolean Algebra Calculator
• Conditional Statement Calculator
• Modus Ponens Validity Checker

What is a logic proof calculator?

A logic proof calculator is a digital tool designed to help students, mathematicians, and computer scientists verify the truth value of logical statements. By inputting the values of individual propositions (variables like P and Q) and selecting a logical operator, the calculator computes the resulting truth value based on the rules of formal logic.

These tools are essential for understanding the structure of arguments. Whether you are solving a math problem involving “If-Then” statements or debugging a complex boolean condition in computer programming, a logic calculator ensures your reasoning follows the strict laws of deduction without human error.

How to Calculate Logic Proofs (Example)

Suppose you want to prove the result of a Conditional Statement (Implication): “If it rains (P is True), then the ground is wet (Q is False).”

1. Identify P: Set P to “True” (It is raining).
2. Identify Q: Set Q to “False” (The ground is not wet).
3. Select Operator: Choose “IMPLIES” (→).
4. Calculate: The logic proof calculator evaluates True → False.
5. Result: The result is False. (It is logically impossible for the premise to be true and the conclusion false in a valid implication).

Frequently Asked Questions (FAQ)

What is the symbol for “Implies” in logic?
The standard symbol is an arrow (→) or a horseshoe (⊃). In this logic proof calculator, we use the standard “Implies” option.

Can this calculator handle complex proofs?
This module focuses on binary operations between two variables (P and Q). For complex multi-step proofs, you would break the equation down into these smaller binary pairs.

What does “Tautology” mean?
A tautology is a logical statement that is always true, regardless of the truth values of its individual parts (e.g., P OR NOT P).

Why is False Implies True result in True?
In formal logic, a conditional statement is only false if the first part (antecedent) is true and the second part (consequent) is false. If the starting assumption is false, the statement is “vacuously true.”