IB Mathematics Analysis and Approaches Question Type 1: Using Counter Examples Exercises

Provide a counterexample to the statement: If $A$ and $B$ are sets, then $A\setminus B=B\setminus A$.

Provide a counterexample to the statement: If $f$ and $g$ are odd functions, then their product $fg$ is odd.

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.