Easy -1.8 This is a straightforward recall question about proof by contradiction methodology requiring no calculation or problem-solving. Students only need to recognize that proof by contradiction assumes the negation of what they want to prove, making this significantly easier than average A-level questions.
4 Millie is attempting to use proof by contradiction to show that the result of multiplying an irrational number by a non-zero rational number is always an irrational number.
Select the assumption she should make to start her proof.
Tick ( \(\checkmark\) ) one box.
Every irrational multiplied by a non-zero rational is irrational. □
Every irrational multiplied by a non-zero rational is rational. □
There exists a non-zero rational and an irrational whose product is irrational. □
There exists a non-zero rational and an irrational whose product is rational. □
4 Millie is attempting to use proof by contradiction to show that the result of multiplying an irrational number by a non-zero rational number is always an irrational number.
Select the assumption she should make to start her proof.\\
Tick ( $\checkmark$ ) one box.
Every irrational multiplied by a non-zero rational is irrational. □
Every irrational multiplied by a non-zero rational is rational. □
There exists a non-zero rational and an irrational whose product is irrational. □
There exists a non-zero rational and an irrational whose product is rational. □
\hfill \mbox{\textit{AQA Paper 1 2021 Q4 [1]}}