Question

Use the definitions of even and odd numbers to justify your answers for (a)-(c). Assume that c is a particular integer.

(a) Is −8c an even integer?
A. Yes, because −8c = 2(−4c) + 1 and −4c is an integer.
B. Yes, because −8c = 2(−4c) and −4c is an integer.
C. No, because −8c = 2(−4c) + 1 and −4c is an integer.
D. No, because −8c = 2(−4c) and −4c is an integer.

Answer 1

The correct answer is B. Yes, because −8c = 2(−4c) and −4c is an integer.

Step-by-step explanation:

In mathematics, an even number is defined as an integer that is divisible by 2 without leaving a remainder. On the other hand, an odd number is not divisible by 2. Let's analyze the given expression −8c. To determine if it is an even integer, we can express it as −8c = 2(−4c). This shows that −8c is a multiple of 2, specifically 2 times −4c. Since −4c is an integer, −8c is also an integer divisible by 2, making it an even number.

Therefore, option B is correct. It states that −8c is an even integer because it can be represented as the product of 2 and another integer (−4c). Options A, C, and D involve adding or subtracting 1, which is unnecessary in this case. The key factor is the presence of the factor 2 in the expression, indicating divisibility by 2 and confirming that −8c is indeed an even integer.