Each question contains six statements followed by four sets of combinations of three. Choose the set in which the statements are logically related.
(A) Some intellectuals are shy and retiring people.
(B) Some shy and retiring people are successful politicians.
(C) No intellectuals are successful politicians.
(D) All shy and retiring people are intellectuals.
(E) Some successful politicians are intellectuals.
(F) No shy and retiring people are successful politicians.
Solution
The logical consistency of the combination CDF is derived from a standard syllogistic structure where the first two statements act as premises that necessarily lead to the third statement as a conclusion. Statement (D) establishes a universal relationship by asserting that "All shy and retiring people are intellectuals," which places the entire group of shy and retiring people within the larger category of intellectuals. Statement (C) provides a negative universal constraint, stating that "No intellectuals are successful politicians," effectively creating a barrier between the intellectual category and the group of successful politicians. Since all shy and retiring people are contained within the intellectual group, and no intellectuals can be successful politicians, it logically follows that no member of the shy and retiring group can be a successful politician either. This direct deduction perfectly matches statement (F), "No shy and retiring people are successful politicians," making the set a valid logical argument.
