Question

Statements: 1. Some actors are singers.
2. All the singers are dancers.

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

Hint:

Use Venn diagrams for syllogism: if the first statement connects A and B, and the second connects B and C, you can infer a relation between A and C when there's overlap.

Answer 1

The Correct Option is A

Step 1: Diagram the statements.
From statement 1: Some actors $\cap$ singers $\neq \emptyset$.
From statement 2: All singers $\subset$ dancers. Step 2: Test Conclusion I.
We know some actors are singers, and all singers are dancers. Therefore, these actors (who are singers) are also dancers. $$ “Some actors are dancers” is true. Step 3: Test Conclusion II.
“No singer is an actor” contradicts statement 1, which says “Some actors are singers.” $$ Conclusion II is false. \[ \boxed{\text{Only (a) follows — Option A}} \]