One of the easiest methods to proof that conjecture is false is to use a counterexample.
So, in this case, we will try to find a counterexample.
We know that √2 is an irrational number.
√2 x √2 = 2
The number 2 is a rational number. Therefore, the product of two irrational numbers is not necessary an irrational number ∎
- Use a direct proof to show that the sum of two even integers is even
- Use a direct proof to show that the sum of two odd integers is even
- Use a proof by contradiction to prove that the sum of an irrational number and a rational number is irrational
- Show that if n is an integer and n^3+5 is odd, then n is even using a proof by contraposition and a proof by contradiction
- Prove that if m and n are integers and mn is even, then m is even or n is even