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 - AQA - A-Level Maths Pure - Question 4 - 2021 - Paper 1

This is the correct assumption that Millie should make to start her proof by contradiction. By assuming the existence of a non-zero rational number and an irrational number whose product is rational, Millie can demonstrate a contradiction if her goal is to show the product is always irrational. This approach allows her to argue that if such a product exists, it contradicts the initial assertion that the product of an irrational number and a non-zero rational is always irrational.