A student has tried to prove the following statement by contradiction: βFor all even integers and , their product is divisible by 4.β The studentβs working is shown below.
- Assumption: All integers such that is odd are even.
- is even; so, write
- Then, , so is even.
- This contradicts the assumption that is odd.
- Therefore, if is odd, then must be odd.
Identify the error in their working.
- AIn the final sentence, they have drawn the wrong conclusion.
- BIn the second sentence, they should have written and .
- CIn the first sentence, they have given the incorrect negation of the statement they want to prove.
- DIn the fourth sentence, they have stated the wrong assumption.
- EIn the third sentence, the algebra is incorrect.
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