1. **Problem:** 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:** None of the options exactly match only iii, so the correct choice is (গ) ii ও iii is false because ii is false, (খ) i ও iii is false because i is false, (ক) i ও ii is false, (ঘ) i, ii ও iii is false. So only iii is true, but no option matches only iii. Hence, the correct answer is none of the above. Final answer: Only statement iii is correct.