Question

6 which term best describes a proof in which you assume the opposite of what you want to prove? a. proof by contradiction b. proof by syllogism c. proof by contrapositive d. proof by converse

Explanation:

• Option A: Proof by contradiction involves assuming the opposite of the statement you want to prove (the negation) and then showing that this assumption leads to a contradiction, which implies the original statement must be true.
• Option B: A syllogism is a form of deductive reasoning with two premises and a conclusion, not related to assuming the opposite.
• Option C: Proof by contrapositive involves proving the contrapositive of a statement (if not - q, then not - p) instead of the original (if p, then q), not assuming the opposite of the conclusion.
• Option D: The converse of a statement is a different statement (if q, then p for original if p, then q), and proof by converse is not a standard proof technique involving assuming the opposite.

Answer:

A. Proof by contradiction