gen-define-natural-deduction-and-give-one-short-worked-example-7785

Define natural deduction and give one short worked example.

# Natural Deduction **Natural deduction** is a proof system in logic where you derive conclusions from premises using a set of inference rules that mirror natural reasoning patterns. Each logical connective (∧, ∨, →, ¬, etc.) has **introduction rules** (how to prove it) and **elimination rules** (how to use it). ## Short Worked Example **Prove:** From premises P → Q and P, derive Q. **Proof:** ``` 1. P → Q Premise 2. P Premise 3. Q →-Elimination (Modus Ponens) on lines 1, 2 ``` **Explanation:** The →-Elimination rule says if you have a conditional (P → Q) and you have its antecedent (P), you can derive its consequent (Q). This is the logical rule known as *modus ponens*. The proof shows the step-by-step derivation with each line justified by either being a premise or following from previous lines by a specific rule.