List all the subsets of S. You may use "C" for chocolate, "V" for vanilla, and "M" for mint. S = {Chocolate, Vanilla, Mint}

I do not understand how to do this.

To list all the subsets of a given set, you need to consider all possible combinations of the elements in the set. Here's how you can approach this problem:

Step 1: Start with an empty set. This represents the subset containing no elements.

Step 2: Consider the first element, "C" (chocolate). You have two choices: include it in the subset or exclude it.

Step 3: For each choice made in Step 2, consider the next element, "V" (vanilla). Again, you have two choices: include it or exclude it.

Step 4: For each choice made in Step 2 and Step 3, consider the last element, "M" (mint). Similarly, you have two choices: include or exclude.

Step 5: Repeat this process for each combination of choices you made. This will give you all possible subsets of the set {C, V, M}.

Let's work through the steps to find all the subsets:

Step 1: Start with an empty set: {}

Step 2: Consider the first element, "C":
- Include "C": {C}
- Exclude "C": {}

Step 3: Consider the second element, "V":
- Include "V" and "C": {C, V}
- Include "V" and exclude "C": {V}
- Exclude "V" and include "C": {C}
- Exclude both "V" and "C": {}

Step 4: Consider the third element, "M":
- Include "M", "V", and "C": {C, V, M}
- Include "M", "V", and exclude "C": {V, M}
- Include "M", exclude "V", and include "C": {C, M}
- Include "M", and exclude both "V" and "C": {M}
- Exclude "M", include "V", and include "C": {C, V}
- Exclude "M", include "V", and exclude "C": {V}
- Exclude "M", exclude "V", and include "C": {C}
- Exclude all: {}

So, the subsets of the set {C, V, M} are: {}, {C}, {V}, {M}, {C, V}, {C, M}, {V, M}, {C, V, M}.

Each subset represents a combination of the elements in the original set. I have explained the process step-by-step, but you can also use coding or mathematical formulas to generate subsets for larger sets.