Question

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

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.

Explanation:

The conjecture is true because, if we multiply two numbers, then their product is greater than either number. As given in the example, 7 × 4 = 28. 28 is greater than both 7 and 4.

Also, if we multiplied a fraction by a whole number, the result would be less than one of the numbers. For example 1/2 × 4 = 2. 2 is greater than 1/2 but not 4. So, the conjecture is false.

If we multiply two fractions, the result is less than both fractions. For example 1/2 × 1/4 = 1/8. 1/8 is less than both 1/2 and 1/4. So, the conjecture is false.

The precious two examples show that there are counterexamples which prove that the conjecture is false although it is true sometimes.