Question

Write a counter example to show that the conjecture is false. (Hint. zero is not positive) conjecture:

The product of two positive numbers is greater than the sum of two numbers.

Answer 1

A counterexample using the numbers 1/2 and 1/3 proves the conjecture false, as their product is less than their sum.

Step-by-step explanation:

The conjecture that the product of two positive numbers is always greater than their sum is not always true. To find a counterexample, we can consider two small fractions such as 1/2 and 1/3. When we multiply these numbers, we get 1/2 × 1/3 = 1/6, which is clearly less than the sum of the two numbers, 1/2 + 1/3 = 5/6. This counterexample shows that the initial conjecture can be false.