The owner of a music store is planning a window display of five products. Three are to be CDs selected from K, L, M, N and O and two are to be DVDs selected from R, S, T and U. The display items are to be selected according to the following conditions: (1) If K is displayed, U must be displayed. (2) M cannot be displayed unless both L and R are also displayed. (3) If N is displayed, O must be displayed, and if O is displayed, N must be displayed. (4) If S is displayed, neither T nor U can be displayed. If T and U are displayed, which of the following must also be displayed?
A. K
B. L
C. M
D. N
E. R
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Explanation: (A) Display must include T (DVD) and U (DVD). The 2 DVDs are set: {T, U}. Since U is selected, S cannot be selected (Condition 4). We need 3 CDs from {K, L, M, N, O}. Since U is selected, K must be selected (Condition 1, converse). The CD set must contain K. Since R is not selected, M cannot be selected (Condition 2). The remaining CDs must be from {L, N, O}. We need 2 more CDs. (3) \(N \iff O\): N and O must be selected together. If L is selected (1 CD), we still need 1 more CD, but N and O must be a pair. So L is excluded. Therefore, the last two CDs must be N and O. The required CD set is {K, N, O}. The full display is {K, N, O, T, U}. The item that **must** be displayed is K.
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