Given : One of them has three books, another one is having six, the third one is having nine, and the fourth one is having twelve books. 1. B is having fewer books than C B < C2. D is having more books than AD > A3. C has fewer books than DC < DNow, we can say that D has the maximum number of books among them all.So, D has 12 books.Now, there are three cases.Case (1):If C has 9 books then B has 6 books and A has 3 books.C = 9 Books, B = 6 Books, A = 3 Books Case (2):If C has 9 books then B has 3 books and A has 6 books.C = 9 Books, B = 3 Books, A = 6 Books Case (3):If C has 6 books then B has 3 books and A has 9 books.C = 6 Books, B = 3 Books, A = 9 Books Now, we check each statement.(a) A and B together must have at least 12 books ? Not necessarily trueBecause- Case (1): A + B = 3 + 6 = 9 (Not true)Case (2): A + B = 6 + 3 = 9 (Not true)Case (3): A + B = 9 + 3 = 12 (True)(b) D and A together must have at least 15 books ? Necessarily true Because- Case (1): D + A = 12 + 3 = 15 (True)Case (2): D + A = 6 + 12 = 18 (True)Case (3): D + A = 12 + 9 = 21 (True)(c) C and D together must have at least 18 books ? Necessarily trueBecause- Case (1): C + D = 9 + 12 = 21 (True)Case (2): C + D = 9 + 12 = 21 (True)Case (3): C + D = 6 +12 = 18 (True)(d) C and B together must have at least 9 books ? Necessarily true Because- Case (1): C + B = 9 + 6 = 15 (True)Case (2): C + B = 9 + 3 = 12 (True)Case (3): C +B = 6 + 3 = 9 (True)Thus, only (a) is not necessarily true.Hence, the correct answer is "only (a)".