All professors are researchers. Some scientists are professors. Which of the given conclusions is logically valid and is inferred from the above arguments:
Options:
(A) All scientists are researchers
(B) All professors are scientists
(C) Some researchers are scientists
(D) No conclusion follows
Official Answer Key:
C
Step-by-Step Solution & Explanation
"Some scientists are professors" combined with "All professors are researchers" gives, by a valid categorical syllogism (Darii-type: Some S are P, All P are R ⇒ Some S are R), the conclusion "Some scientists are researchers". This converts validly (particular affirmative propositions convert directly) to "Some researchers are scientists". (A) is an invalid universal generalization from a particular premise; (B) reverses a premise incorrectly. Answer: (C) Some researchers are scientists.
Section 1 — Engineering Mathematics
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.