If E = {1, 2, 3, 4, 5}, how many subsets of E contain the element 1?

If E = {1, 2, 3, 4, 5}, how many subsets of E contain the element 1?

Correct Answer: 16

Step 1: Identify the set E, which is {1, 2, 3, 4, 5}.
Step 2: We want to find subsets that must include the element 1.
Step 3: Since 1 is included in every subset we are considering, we only need to focus on the remaining elements, which are {2, 3, 4, 5}.
Step 4: Count the number of remaining elements, which is 4 (the elements are 2, 3, 4, and 5).
Step 5: Each of the 4 remaining elements can either be included in a subset or not included. This gives us 2 choices (include or not include) for each element.
Step 6: To find the total number of combinations of the remaining elements, we calculate 2 raised to the power of the number of remaining elements: 2^4.
Step 7: Calculate 2^4, which equals 16. This means there are 16 different subsets of E that contain the element 1.

Subsets – Understanding how to calculate the number of subsets of a set, particularly when certain elements must be included.
Combinatorics – Applying the principles of combinatorics to determine the number of ways to choose elements from a set.