To list all possible subsets of $A = \{a, b, c, d, e\}$ that include both elements $a$ and $b$, we need to include $a$ and $b$ in every subset and add any combination of the remaining elements. Here is the complete set of subsets in roster notation:

Subsets of $A$ containing $\{a, b\}$:

1. $\{a, b\}$
2. $\{a, b, c\}$
3. $\{a, b, d\}$
4. $\{a, b, e\}$
5. $\{a, b, c, d\}$
6. $\{a, b, c, e\}$
7. $\{a, b, d, e\}$
8. $\{a, b, c, d, e\}$

These subsets account for all possible combinations of the set $\{c, d, e\}$ alongside $a$ and $b$.

Would you like more details or have further questions?

5 Related Questions:

1. How many subsets exist in general for a set with 5 elements?
2. What is the general formula for the number of subsets containing specific elements in a set?
3. Can we calculate subsets for larger sets efficiently?
4. How does the inclusion-exclusion principle relate to subset selection?
5. How do subsets differ when order matters (permutations)?

Tip:

To calculate subsets of a given set containing specific elements, you can fix those elements and generate combinations from the remaining elements.