Question

which of the following sets would belong to the integer subset but NOT the whole number subset of real numbers?

F.[-4, -3 , 1.25]
G.[-3, -21/3, -5]
H. [3, -6, 7]
J.[√4, 6, -7]

Answer 1

To determine which set belongs to the integer subset but NOT the whole number subset of real numbers, we first need to clarify the definitions of integers and whole numbers.

- **Integers** are all whole numbers and their negative counterparts: {..., -3, -2, -1, 0, 1, 2, 3, ...}.
- **Whole numbers** are all non-negative integers: {0, 1, 2, 3, ...}.

Now, let's evaluate each set:

**F. [-4, -3, 1.25]**
- Contains -4 (integer), -3 (integer), and 1.25 (not an integer).
- This set does not consist only of integers.

**G. [-3, -21/3, -5]**
- Contains -3 (integer), -21/3 = -7 (integer), and -5 (integer).
- This set consists only of integers, but since they are all negative, they do not belong to the whole number subset.

**H. [3, -6, 7]**
- Contains 3 (integer), -6 (integer), and 7 (integer).
- This set consists of integers, but the presence of -6 means it does not belong to whole numbers.

**J. [√4, 6, -7]**
- Contains √4 = 2 (integer), 6 (integer), and -7 (integer).
- This set consists of integers, but includes -7, meaning it does not belong to whole numbers.

The only set that consists entirely of integers and does NOT belong to the whole number subset is:

**G. [-3, -21/3, -5]**

Therefore, the answer is **G**.