Question Type 1: Using counter examples Exercises

Provide a counterexample to the statement that all prime numbers are odd.

Provide a counterexample to the statement that the sum of two even integers is odd.

Provide a counterexample to the statement that for all real $x$, $x^2 \ge x$. [2 marks]

Provide a counterexample to the statement that the product of two irrational numbers is always irrational.