We use proofs to show that a mathematical statement is true. The most common form of a mathematical statement is the if-then statement. Here are examples of a true statement and a false statement with a counterexample: True statement: If a number is divisible by 2, then it’s even.
False statement: If a number is divisible by 3, then it’s odd.
Counterexample: The number 12 is divisible by 3 (12 ÷ 3 = 4), but 12 is an even number (not odd).
Give an example of a true mathematical statement and a false mathematical statement in if-then form. Include a counterexample with the false statement showing that the example isn’t true.