gen-in-3-4-sentences-explain-proof-by-contradiction-state-any-ke-93ae

In 3-4 sentences, explain proof by contradiction. State any key formula.

# Proof by Contradiction Proof by contradiction is a logical technique where you assume the opposite of what you want to prove, then show this assumption leads to a logical impossibility or contradiction. Once a contradiction is reached, you conclude that the original assumption must be false, therefore the original statement must be true. The key logical formula is: To prove statement P, assume ¬P (not P) and derive a contradiction (Q ∧ ¬Q). Since a contradiction cannot be true, we conclude ¬P is false, therefore P must be true. A classic example is proving √2 is irrational by assuming it's rational, which eventually leads to the contradiction that an integer must be both even and odd.