Institution: জগন্নাথ বিশ্ববিদ্যালয় Exam: C ইউনিট : 2017-2018
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To understand why the correct answer to the question is "D) কোনোটিই নয়," let's analyze each option based on set theory principles.

1. **A ∪ A = A**: This statement is true because the union of a set with itself does not add any new elements; it simply results in the original set.

2. **A ∩ A = A**: This statement is also true. The intersection of a set with itself returns the set itself, as all elements of A are included.

3. **A ∩ ∅ = A**: This statement is false. The intersection of any set A with the empty set (∅) results in an empty set (∅), as there are no elements common to both A and ∅.

Since options A and B are true and option C is false, we have to consider the phrase "একটি সত্য নয়," which means "one that is not true." The presence of one false statement among them might tempt one to choose the option that indicates it's incorrect. However, because options A and B are both correct and C is the only incorrect one, "D) কোনোটিই নয়" suggests none of these is entirely false, which could imply that the statement is talking about all needing to be false to choose an option.

Thus, because options A and B are valid statements, the best choice is indeed **"D: কোনোটিই নয়,"** indicating the misleading nature of the question.