Question

Statements:
All pens are pencils.
No pencil is marker.

Conclusions:
(1) Some pens are markers.
(2) Some pens are pencils.

• A. Neither I nor II follows
• B. Only II follows
• C. Either I or II follows
• D. Both I and II follow

Hint:

In syllogisms, a conclusion that contradicts a definite inference from the statements is always false. Also, "All A are B" implies "Some A are B".

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a syllogism problem. We must determine which conclusions can be logically derived from the given statements.
Step 2: Detailed Explanation:
Let's analyze the statements using a Venn Diagram approach.

"All pens are pencils." This means the circle representing "pens" must be completely inside the circle representing "pencils".
"No pencil is marker." This means the circle for "pencils" and the circle for "markers" must be completely separate, with no overlap. From this combined information, since the "pens" circle is inside the "pencils" circle, and "pencils" are completely separate from "markers", it logically follows that "pens" must also be completely separate from "markers". The definite conclusion is "No pen is a marker".
Now let's evaluate the given conclusions:

Conclusion (1): Some pens are markers. This is a direct contradiction to our derived conclusion "No pen is a marker". Therefore, conclusion (1) is false.
Conclusion (2): Some pens are pencils. The statement given is "All pens are pencils". In logic, if a universal affirmative statement ("All A are B") is true, the particular affirmative ("Some A are B") is also considered true, assuming that the set 'A' is not empty. Therefore, conclusion (2) is true. Step 3: Final Answer:
Only conclusion (2) logically follows from the statements.