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.
13 answers