Question

3. Read the conjecture below. Select all of the true statements about this conjecture. If you multiply two numbers, then the product is greater than either number. Select all that apply. a. This conjecture is true. For example, (7)(4) = 28. The product of 28 is greater than 7 and greater than 4. b. This conjecture is false. There is a counterexample that would prove this conjecture false. c. This conjecture is false: . d. There is not enough information.

Answer 1

This conjecture is false. There is a counterexample that would prove this conjecture false.

Explanation:

Given the conjecture that if you multiply two numbers, then the product is greater than either number is very false. There is a counterexample that would prove this conjecture false.

The counter example is as shown;

Let the two numbers be 1 and 2.

Take their product;

1(2) = 2

We can see that their product which is 2 although greater than 1 is not greater than the other number but equal to it. This example therefore counter the conjecture. This is applicable to numbers with 1 included.