Question

geometry 1 - maxwell (lms) lesson 1-4 additional practice (lms graded) find a counterexample to show that the statement is incorrect. the product of any two counting numbers is divisible by 2. choose the correct answer below. ○ a. 3×4 = 12, which is not divisible by 2. video textbook get more help ▲ review progress question |

Explanation:

Step1: Analyze the statement

The statement claims the product of any two counting numbers is divisible by 2. We need a counterexample, i.e., two counting numbers whose product is not divisible by 2.

Step2: Evaluate Option A

For option A: \(3\times4 = 12\). But \(12\div2=6\), so 12 is divisible by 2. Wait, maybe there's a typo or we need to find a correct counterexample. Let's think: counting numbers start at 1. Take 1 and 3: \(1\times3 = 3\), and \(3\div2 = 1.5\), so 3 is not divisible by 2. But in the given options, maybe the intended correct counterexample (though option A as written is wrong, but perhaps a misprint). Wait, maybe the original problem had a different option, but assuming we need to find a counterexample, a correct one would be \(1\times3 = 3\) (not divisible by 2). But since the option given is A (even though the explanation in A is wrong, maybe a mistake), but actually, a correct counterexample is two odd counting numbers, like 3 and 5: \(3\times5 = 15\), \(15\div2 = 7.5\), not divisible. But in the given options, maybe the intended answer is a counterexample, so if we consider that maybe the option A has a mistake, but the idea is to find two odd numbers. However, based on the given option, perhaps there's an error, but the correct counterexample would be a product of two odd counting numbers, like \(3\times5 = 15\) (not divisible by 2). But since the option A is given, maybe it's a mistake, but the process is to find two counting numbers (odd) whose product is odd (not divisible by 2).

Answer:

A correct counterexample is \(3\times5 = 15\) (not divisible by 2). But based on the given option (even with the error in A's explanation), if we assume a typo, the intended answer would be a product of two odd numbers. However, the option A as written is incorrect (12 is divisible by 2), so perhaps there's a mistake in the problem's options. But the correct counterexample is the product of two odd counting numbers, e.g., \(1\times3 = 3\), \(3\times5 = 15\), etc.