Pearson Edexcel IAL Mathematics P2.1.3 Disproof by counter example

Practise disproving universal statements by choosing one valid value or example, calculating the result and stating why the claim fails.

Exam points

choose a valid counterexample, then show the resulting value is not prime or not divisible
use real, negative or irrational values to make a stated algebraic claim fail

[Maximum number: 1]

A student states
"If x and y are irrational numbers, $x \neq y$ , then x y is also irrational."

Show, by counter example, that this statement is not always true.

Provides a counterexample, for example
$\sqrt2\times\sqrt8=4$
B1: provides a counterexample and shows that the statement is not always true. The result must be written in rational form.
[1]

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P2.1.3 - Disproof by counter example question 1