1. What Is A Logical Proof?

A logical proof is a sequence of statements that demonstrates the validity of a conclusion based on given premises using established rules of inference. It represents a formal method of reasoning that ensures conclusions follow necessarily from their premises.

2. How The Proof Calculator Works

The calculator applies formal rules of inference to derive conclusions:

Supported rules include:

• Modus Ponens: From P → Q and P, conclude Q
• Modus Tollens: From P → Q and ¬Q, conclude ¬P
• Hypothetical Syllogism: From P → Q and Q → R, conclude P → R

3. Importance Of Logical Proofs

Details: Logical proofs are fundamental to mathematics, computer science, philosophy, and legal reasoning. They provide a rigorous method for establishing truth and validity in argumentation.

4. Using The Calculator

Tips: Enter your premises in logical notation (e.g., "P → Q", "¬Q"), select the appropriate rule of inference, and the calculator will derive the valid conclusion.

5. Frequently Asked Questions (FAQ)

Q1: What is modus ponens?
A: Modus ponens is a rule of inference that states if P implies Q, and P is true, then Q must be true.

Q2: How is modus tollens different?
A: Modus tollens states if P implies Q, and Q is false, then P must be false.

Q3: What is hypothetical syllogism?
A: Hypothetical syllogism allows chaining implications: if P implies Q and Q implies R, then P implies R.

Q4: Can this prove any logical argument?
A: This calculator handles basic inference rules. Complex proofs may require multiple steps or additional rules.

Q5: What notation should I use?
A: Use standard logical notation: → for implication, ¬ for negation, ∧ for conjunction, ∨ for disjunction.