Final Answer:
b) No, because dividing integers can sometimes result in a non-integer.
Step-by-step explanation:
The set of integers is not closed with respect to division. While it is true that dividing two integers can result in an integer in some cases, it is not always guaranteed. Consider the example of dividing 5 by 2; the result is 2.5, which is not an integer. Therefore, option (b) is the correct choice.
When we divide two integers, the result may be a fraction or a decimal, not necessarily an integer. This is evident in cases where the numerator is not a multiple of the denominator. For instance, dividing 7 by 2 yields 3.5. In mathematical terms, the set of integers lacks closure under division because the result may fall outside the set.
To further illustrate, let's take the division of 8 by 3. The result is 2.666..., which is a recurring decimal and clearly not an integer. This deviation from integer values demonstrates that the set of integers is not closed under division. In conclusion, option (b) accurately captures this characteristic, highlighting the instances where dividing integers can indeed lead to non-integer results.