In a proof by contradiction, once a contradiction has been reached, what can be concluded?
Answer and explanation
Correct answer: E. The initial assumption is false
- Step 1: The working from the assumption was logically valid, so the contradiction must come from the assumption itself.
- Step 2: Hence the assumption (the negation of the claim) is false, which means that the original claim is true.
Answer
The initial assumption is false.
Why not the others: A contradiction does not show that the original statement is false; it shows that the assumed negation is impossible. Valid working cannot be to blame, so there is no error to find. The assumption and the original statement cannot both be true, because the assumption was the negation of the statement. And something can be concluded: that the original statement is true.
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