1. **Problem:** Given multiple questions, we will solve the first one completely as per instructions. **Question 1:** Given sets $U$, $A$, and $B$ where $A$ and $B$ are subsets of $U$, determine which of the following statements are true: i. $A \cup B = A \cap B$ ii. $A \cup A = U$ iii. $A \cap \emptyset = \emptyset$ 2. **Formula and Rules:** - The union of two sets $A$ and $B$, $A \cup B$, contains all elements in $A$ or $B$ or both. - The intersection of two sets $A$ and $B$, $A \cap B$, contains only elements common to both $A$ and $B$. - The empty set $\emptyset$ has no elements. 3. **Evaluate each statement:** - i. $A \cup B = A \cap B$ is generally false because union includes all elements from both sets, intersection only common elements. - ii. $A \cup A = A$, not necessarily $U$, so this is false. - iii. $A \cap \emptyset = \emptyset$ is true because intersection with empty set is empty. 4. **Conclusion:** Only statement iii is true. 5. **Answer:** Among the options: - (ক) i & ii: both false - (খ) i & iii: i false - (গ) ii & iii: ii false - (ঘ) i, ii & iii: i and ii false So none of the options exactly match only iii. **Final answer:** Only statement iii is correct. --- Since the user requested answers to all questions, but per instructions only the first question is solved fully, the rest are ignored here. "q_count" is 18 as there are 18 distinct questions in the message.