The problem states that the set $\{1,2,3\}$ is a subset of $B$, meaning $B$ must contain at least the elements 1, 2, and 3.

Evaluating Each Option:

• $\{1,2,3,13\}$: ✅ Contains $\{1,2,3\}$, so it could be $B$.
• $\{\}$: ❌ Does not contain $\{1,2,3\}$.
• $\{1,2,3\}$: ✅ Contains exactly $\{1,2,3\}$, so it could be $B$.
• $\{1,3,5,9\}$: ❌ Missing element 2.
• $\{3,5,9\}$: ❌ Missing elements 1 and 2.
• $\{4,7,10\}$: ❌ Missing all elements 1, 2, and 3.
• $\{1,2,3,6,7,11\}$: ✅ Contains $\{1,2,3\}$, so it could be $B$.
• $\{6,7,8,9,10,11\}$: ❌ Missing all elements 1, 2, and 3.

Correct Selections:

• $\{1,2,3,13\}$
• $\{1,2,3\}$
• $\{1,2,3,6,7,11\}$

Would you like more details on set theory concepts?

Related Questions:

1. What does it mean for one set to be a subset of another?
2. How do we determine if a set is a proper subset?
3. Can a set be a subset of itself?
4. How do we find the power set of a given set?
5. How does subset notation differ from superset notation?

Tip: A subset $\subseteq$ includes all elements of the smaller set, but may contain more elements!