List all the subsets of the given set.
(seal, yak, goat}
Choose the correct answer below.
O A. Ø, (seal), {yak}, {goat), (seal, yak}, {seal, goat), {yak, goat), (seal, yak, goat}
O B. Ø, (seal), (yak}, {goat), (seal, yak}, {seal, goat), (yak, goat}
O C. (seal), {yak), {goat), (seal, yak}, {seal, goat}, {yak, goat}
O D. (seal}, {yak}, {goat), {seal, yak}, {seal, goat), (yak, goat), (seal, yak, goat)
The correct answer is D. (seal), {yak}, {goat}, {seal, yak}, {seal, goat}, {yak, goat}, (seal, yak, goat).
The answer is option D:
(subset containing one element) Ø, (seal), (yak), (goat),
(subsets containing two elements) {seal, yak}, {seal, goat}, {yak, goat},
(subsets containing all three elements) {seal, yak, goat}
To find all the subsets of a given set, you can use the following approach:
1. Start with an empty set ({}) as the first subset.
2. For each element in the given set, consider two possibilities: either include the element in the subset or exclude it.
3. Generate new subsets by including or excluding each element, using the elements from the previous step.
4. Repeat the process until you have considered all elements.
Now, let's apply this approach to the given set ({seal, yak, goat}):
1. Start with an empty set: {}
2. Consider the first element, "seal".
- Include "seal" in the subset: {seal}
- Exclude "seal" from the subset: {}
3. Consider the second element, "yak".
- Include "yak" in the subset: {yak}
- Exclude "yak" from the subset: {}
4. Consider the third element, "goat".
- Include "goat" in the subset: {goat}
- Exclude "goat" from the subset: {}
5. Combine all possibilities:
- {}, {seal}, {yak}, {goat}, {seal, yak}, {seal, goat}, {yak, goat}, {seal, yak, goat}
Therefore, the correct answer is option D:
- (seal}, {yak}, {goat}, {seal, yak}, {seal, goat), (yak, goat), (seal, yak, goat)