Syllogism (logical deduction): Evaluate the conclusions based on the given statements. Statements: S1: Some actors are singers. S2: All the singers are dancers. Conclusions: C1: Some actors are dancers. C2: No singer is actor. Choose the option that correctly identifies which conclusion(s) follow.

Given data

• S1: Some actors are singers.
• S2: All singers are dancers.
• Conclusions to test: C1 (Some actors are dancers), C2 (No singer is actor).

Concept / Approach
Use set relations: If some Actors ∩ Singers ≠ ∅ and Singers ⊆ Dancers, then those same actors are also Dancers. A universal negative about singers vs actors contradicts S1.

Step-by-step check
From S1: ∃x such that x ∈ Actors and x ∈ Singers. From S2: Singers ⊆ Dancers ⇒ Any singer is a dancer. Therefore that x is also a Dancer ⇒ Some actors are dancers ⇒ C1 is true. C2 says “No singer is actor,” which directly contradicts S1 ⇒ C2 is false.

Common pitfalls
Assuming “some” means “all,” or overlooking subset propagation (Singers ⊆ Dancers).

Final Answer
Only conclusion I follows.