If E = {a, b, c}, how many subsets of E contain the element 'a'?

If E = {a, b, c}, how many subsets of E contain the element 'a'?

Step 1: Identify the set E, which is {a, b, c}.
Step 2: Since we want subsets that contain the element 'a', we will always include 'a' in our subsets.
Step 3: Look at the remaining elements in the set after including 'a', which are {b, c}.
Step 4: For each of the remaining elements (b and c), we can either include it in the subset or not include it.
Step 5: List the possible combinations of the remaining elements with 'a':
- If we include neither b nor c, we have the subset {a}.
- If we include b but not c, we have the subset {a, b}.
- If we include c but not b, we have the subset {a, c}.
- If we include both b and c, we have the subset {a, b, c}.
Step 6: Count the total number of subsets that contain 'a': {a}, {a, b}, {a, c}, {a, b, c}.
Step 7: The total number of subsets containing 'a' is 4.

Subsets – Understanding how to form subsets from a set and the role of specific elements in those subsets.
Combinatorics – Applying combinatorial principles to count the number of ways to include certain elements in subsets.