Let S={1,2,3} be a sample space

How many subsets of S contain the number 3?

How many subsets of S contain either the number 2 or 3?

there are 2^3 = 8 subsets of S.

see where that takes you.

To find the number of subsets of S that contain the number 3, we need to consider that for every element in a subset, we have two choices: either include it or exclude it.

For the set S = {1, 2, 3}, let's analyze the subsets containing the number 3:
- Subset {3} contains the number 3.
- Subset {1, 3} contains both elements 1 and 3.
- Subset {2, 3} contains both elements 2 and 3.
- Subset {1, 2, 3} contains all three elements.

Thus, there are 4 subsets of S that contain the number 3: {3}, {1, 3}, {2, 3}, {1, 2, 3}.

Now, let's find the number of subsets of S that contain either the number 2 or 3:
- Subset {2} contains the number 2.
- Subset {3} contains the number 3.
- Subset {2, 3} contains both elements 2 and 3.
- Subset {1, 2, 3} contains all three elements.

Thus, there are 4 subsets of S that contain either the number 2 or 3: {2}, {3}, {2, 3}, {1, 2, 3}.