S = {Chocolate, Vanilla, Mint}
11)
____D_
A)
{Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, {Chocolate}, {Vanilla}, {Mint}
B)
{Chocolate, Vanilla, Mint}, {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, {Chocolate}, {Vanilla}, {Mint}
C)
{Chocolate, Vanilla, Mint}, {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, {Chocolate}, {Vanilla}, {Mint}, { }
D)
{Chocolate, Vanilla, Mint}, {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, Chocolate, Vanilla, Mint
To answer question 11, we need to find all the subsets of the given set S = {Chocolate, Vanilla, Mint}.
A subset is a set that contains elements from the original set (S), but not necessarily all of them.
To find all the subsets, we can use the concept of power set. The power set of a set is the set of all its subsets, including the empty set and the set itself.
To calculate the power set of S, we can use the following formula:
- If the original set S has n elements, then the power set will have 2^n subsets.
In this case, S has 3 elements (Chocolate, Vanilla, Mint), so the power set will have 2^3 = 8 subsets.
Let's go through the options and see which one represents the power set of S:
A) {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, {Chocolate}, {Vanilla}, {Mint}
- This option has 6 subsets, missing the empty set and the set itself. So, it is not the correct answer.
B) {Chocolate, Vanilla, Mint}, {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, {Chocolate}, {Vanilla}, {Mint}
- This option has 7 subsets, but it is missing the empty set. So, it is also not the correct answer.
C) {Chocolate, Vanilla, Mint}, {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, {Chocolate}, {Vanilla}, {Mint}, {}
- This option has 8 subsets, including the empty set {}. So, this is a possible correct answer.
D) {Chocolate, Vanilla, Mint}, {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, Chocolate, Vanilla, Mint
- This option does not represent the subsets correctly. It includes individual elements (Chocolate, Vanilla, Mint) instead of sets.
So, the correct answer to question 11 is option C) {Chocolate, Vanilla, Mint}, {Vanilla, Mint}, {Chocolate, Mint}, {Chocolate, Vanilla}, {Chocolate}, {Vanilla}, {Mint}, {}.