Question

Conjecture. For all nonzero integers k, m, and n, if km and kn, then m n . Disprove the conjecture and carefully explain why you know you have shown the conjecture is false.

Answer 1

The conjecture that if km and kn, then m n is false, as shown through a counterexample.

Step-by-step explanation:

The conjecture that if km and kn, then m n is actually false. To disprove this, we can provide a counterexample. Let's take k = 2, m = 3, and n = 4. Now, km = 2*3 = 6 and kn = 2*4 = 8. However, m n = 3 4 = 12, which is not equal to 6 or 8. Hence, the conjecture is disproven.