Question

Some As are Bs and some Bs are Cs. Which of the following is necessarily true? I. Some As are Cs
II. All Cs are As

• A. Only (I) follows
• B. Only (II) follows
• C. Both (I) and (II) follow
• D. Neither I nor II follow

Hint:

In syllogism questions, remember that "Some" does not imply "All," and overlaps do not necessarily extend transitively (A--B and B--C does not imply A--C). Always check necessity versus possibility.

Answer 1

The Correct Option is D

Step 1: Translate the statements
- Statement 1: "Some As are Bs" means there is at least some overlap between sets A and B.
- Statement 2: "Some Bs are Cs" means there is at least some overlap between sets B and C.
Step 2: Check possibility of I: Some As are Cs
From the two premises, we only know that:
- A overlaps with B, and
- B overlaps with C.
But this does not guarantee that A overlaps with C. It may or may not happen depending on the exact Venn diagram.
\(\Rightarrow\) So, I is not \emph{necessarily true}.
Step 3: Check possibility of II: All Cs are As
There is no information suggesting that the entire set C lies inside A. Cs are only partly connected to B.
\(\Rightarrow\) So, II is not \emph{necessarily true}.
Step 4: Conclusion
Neither (I) nor (II) is guaranteed by the given premises.
\(\boxed{\text{Neither I nor II follow}}\)