What is a proof by contradiction?

Problem Statement

What is a proof by contradiction?

Step-by-Step Explanation

Proof by contradiction assumes the opposite of a claim and shows that assumption leads to an impossibility.

1. Identify what the question is asking. In Discrete Math, this usually means naming the known quantities, the unknown quantity, and the concept that connects them.
2. Write the relevant definition, rule, or relationship before substituting numbers or manipulating symbols.
3. Work one step at a time and keep units, signs, and restrictions visible.
4. Check whether the answer makes sense in the original context.

Final Answer

Proof by contradiction assumes the opposite of a claim and shows that assumption leads to an impossibility. The reliable strategy is to start from the definition, apply the correct rule carefully, and then interpret the result in plain language.