Question Type 1: Using counter examples Exercises

Question 1

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

[3]

Question 2

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

[4]

Question 3

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

[2]

Question 4

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

[3]

Question 5

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

[2]

Question 6

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

[2]