Question

In a(n) _____ proof, or proof by _____, you assume the opposite of what you want to prove.

A) Opposite
B) Contradiction
C) Two-column
D) Definition
E) Conjecture

Answer 1

The answer to the question is 'proof by contradiction,' where you assume the negation of what you're trying to prove and show that this assumption leads to a contradiction, thereby proving that the original statement must be true.

Step-by-step explanation:

In a proof by contradiction, you assume the opposite of what you want to prove. This method involves assuming the negation of the statement you aim to prove and demonstrating that this assumption leads to a contradiction. A contradiction occurs when you combine a statement and its negation, resulting in a claim that is always false. For example, saying 'My dog is on her bed and my dog is not on her bed' creates a contradiction. The proof by contradiction is powerful because if an assumption leads to such a contradiction, then the original statement must be true. Therefore, the answer to the student's question is B) Contradiction.