List all subsets of the following set:
{dog, cat, fish}
A. {dog}; {Cat}; {fish}
B. {dog}; {Cat}; {fish}; {dog,cat}; {dog,fish}
C {}; {dog}; {cat}; {fish}; {dog,cat}; {dog,fish}***
D {}; {dog}; {cat}; {fish}; {dog,cat}; {dog,fish}; {cat,fish}; {dog,cat,fish}
ah yes, dog cat, fish. welcome to muth class.
Nope. D
Just FYI - the set of all subsets of a set S is called the power set of S, and if S has n elements, the power set has 2^n elements.
i think is d
To list all subsets of a set, you can use the concept of power set. The power set of a set is a set that contains all possible subsets of the given set, including the empty set and the set itself.
To find the power set, you can follow these steps:
1. Start with an empty set.
2. For each element in the original set, create new subsets by adding that element to the existing subsets.
3. Combine the new subsets with the existing subsets to get the updated list of subsets.
4. Repeat steps 2 and 3 until all elements in the original set have been considered.
Let's apply these steps to the given set {dog, cat, fish}:
Step 1: Start with an empty set: {}
Step 2: Add the first element "dog":
- Existing subsets: {}
- New subsets with "dog": {dog}
Updated subsets: {}, {dog}
Step 3: Combine the new subsets with the existing subsets:
- Updated subsets: {}, {dog}
Step 4: Repeat steps 2 and 3 with the second element "cat":
- Existing subsets: {}, {dog}
- New subsets with "cat": {cat}, {dog, cat}
Updated subsets: {}, {dog}, {cat}, {dog, cat}
Step 3: Combine the new subsets with the existing subsets:
- Updated subsets: {}, {dog}, {cat}, {dog, cat}
Step 4: Repeat steps 2 and 3 with the third element "fish":
- Existing subsets: {}, {dog}, {cat}, {dog, cat}
- New subsets with "fish": {fish}, {dog, fish}, {cat, fish}, {dog, cat, fish}
Updated subsets: {}, {dog}, {cat}, {dog, cat}, {fish}, {dog, fish}, {cat, fish}, {dog, cat, fish}
So, the correct answer is C.
The subsets of {dog, cat, fish} are: {}, {dog}, {cat}, {dog, cat}, {fish}, {dog, fish}, {cat, fish}, {dog, cat, fish}.