Final answer:
All possible subsets of the set (t, h, e, n) can be listed systematically from the empty set to the full set, totaling 16 subsets including single-element, two-element, three-element, and the full four-element subset.
Step-by-step explanation:
The question involves determining all possible subsets of the set (t, h, e, n). A subset is a set that contains elements that are all from another set. There are 2 to the power of the number of elements in the set possible subsets. Since our set has 4 elements, there will be 24 = 16 possible subsets.
To make a systematic list of these subsets, we can start with the smallest subset, the empty set, and gradually add elements until we reach the full set:
- Empty set: {}
- 1-element subsets: {t}, {h}, {e}, {n}
- 2-element subsets: {t, h}, {t, e}, {t, n}, {h, e}, {h, n}, {e, n}
- 3-element subsets: {t, h, e}, {t, h, n}, {t, e, n}, {h, e, n}
- 4-element subset: {t, h, e, n}
These are all the possible subsets of the set (t, h, e, n).