Question

Statements: I. All Actors are Musicians.
II. No Musician is a Singer.
III. Some Singers are Dancers.
IV. Some Dancers are Musicians.

• A. Only (1) conclusion follows
• B. Only (2) conclusion follows
• C. Either (1) or (2) follows
• D. Neither (1) nor (2) follows

Hint:

In syllogisms, contradictory conclusion pairs (Some A are B / No A is B) will always have one true and one false. If both appear, the answer is “Either I or III follows.”

Answer 1

The Correct Option is C

Step 1: Analyze given statements.
From I: Actors $\subset$ Musicians. From II: Musicians $\cap$ Singers = $\varnothing$. Thus, Actors $\cap$ Singers = $\varnothing$ — this directly supports Conclusion III (“No Actor is a Singer”) and contradicts Conclusion I (“Some Actors are Singers”). Step 2: Check Conclusion II.
From IV: Some Dancers are Musicians. From I: Actors $\subset$ Musicians. But there’s no given link between those “some dancers” and actors specifically. So we cannot conclude “Some Dancers are Actors.” Conclusion II does not follow. Step 3: Determine the either–or condition.
Conclusions I and III are exact contradictories: “Some actors are singers” vs “No actor is a singer.” In syllogism, when one is true, the other is false, and they form an either–or} pair. \[ \boxed{\text{Either (I) or (III) follows — matches Option C structure}} \]