Each question contains six statements followed by four sets of combinations of three. Choose the set in which the statements are logically related.
(A) All students are the people who saw the game.
(B) All persons who saw the game are persons who were at dance.
(C) Some students were persons who were at the dance.
(D) Some persons who saw the game are students.
(E) Some students are not the persons who saw the game.
(F) No one who was at the dance saw the game.
Solution
BDC (Correct): If all game-seers were at the dance (B) and some game-seers are students (D), then those specific students must have been at the dance (C).
ABC (Incorrect): This set is redundant; if all students saw the game (A) and all game-seers were at the dance (B), the conclusion should be "All students were at the dance," not just "Some" (C).
ACF (Incorrect): Statement (F) directly contradicts the combination of (A) and (C) by claiming no one at the dance saw the game.
CDA (Incorrect): Knowing some students were at the dance (C) and some game-seers are students (D) provides no logical basis to conclude that all students saw the game (A).
Thus, the correct answer is Option A.
