A cubic storage unit is designed such that its side length, x x\,x meters, is an integer. An engineer claims that if the volume of the unit, V=x3V = x^3V=x3, is a multiple of 3, then the side length x x\,x must be a multiple of 3. Use proof by contradiction to prove that the engineer's claim is correct.
107 exam-style questions on OCR A Level Maths 1.1 Proof, covering 1.1.1 Structure of mathematical proof, 1.1.2 Logical connectives, 1.1.3 Disproof by counter example, 1.1.4 Proof by contradiction (A-level only), and 1.1 Proof. Each one has a worked solution and a mark scheme showing where the marks go.