1. The problem asks us to determine the correct relationship between two sets $A$ and $B$ among the options given: 2. Recall the definitions: - The union $A \cup B$ is the set of all elements in $A$, or in $B$, or in both. - The intersection $A \cap B$ is the set of all elements common to both $A$ and $B$. 3. Important rule: For any two sets $A$ and $B$, the intersection is always a subset of the union, i.e., $$ A \cap B \subseteq A \cup B $$ This is because every element common to both sets is certainly in at least one of them. 4. Let's analyze each option: - a. $A \cup B \subseteq A \cap B$: This would mean every element in the union is also in the intersection, which is false because the union includes elements not common to both. - b. $A \cap B \subseteq A \cup B$: This is true by the rule stated above. - c. $A \cup B = A \cap B$: This would mean the union and intersection are exactly the same, which is generally false unless $A = B$. - d. None of these: Since option b is true, this is false. 5. Therefore, the correct answer is option b. Final answer: $\boxed{A \cap B \subseteq A \cup B}$