Proof by exhaustion

What you'll learn

1. 1

   Proof by exhaustion means checking EVERY possible case. Imagine you have 3 different keys 🗝️ and only one opens the door 🚪. You try each key until the door opens — that's checking all cases!

2. 2

   How many cases do you check in proof by exhaustion?

3. 3

   Test each number from 1 to 5. Which ones are even? Tap each one to check.

4. 4

   Prove: For all integers n from 1 to 4, n² + n is even.

5. 5

   Prove: For all integers n from 1 to 3, n² is odd. Which of these is the correct check?

6. 6

   To prove 'All numbers from 1 to 10 are less than 12' by exhaustion, how many cases do you check?

7. 7

   Which of these statements can be proved by exhaustion?