A proof by contradiction that is irrational begins by assuming the opposite. Which assumption is made?
Answer and explanation
Correct answer: D. where and are integers with no common factor
- Step 1: To prove a statement by contradiction, assume that it is false. The statement is ' is irrational', so we assume is rational.
- Step 2: A rational number can be written in lowest terms , i.e. with and having no common factor. This 'lowest terms' assumption is what the argument later contradicts.
Answer
where and are integers with no common factor.
Why not the others: A proof by contradiction assumes the opposite of the claim, so ' is irrational' (the claim itself) cannot be the assumption; would make an integer, which is only a special case; is a fact, not an assumption; 'both even' is what the argument derives later, contradicting 'no common factor'.
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