Question

Four statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
1. Some hill is land.
2. All land is plateau.
3. Only a few land is peak.
4. Some peak is valley.
Conclusions:
I. Some peak is hill.
II. No hill is peak.

• A. Only conclusion II follows
• B. Only conclusion I follows
• C. Either conclusion I or II follows
• D. Neither conclusion I nor II follows

Hint:

In syllogisms, when you have two conclusions of the form "Some A are B" and "No A are B", and both are individually possible but not definite, it's a classic "Either/Or" case.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is a syllogism problem. We need to use the given statements to determine the validity of the two conclusions. We can use Venn diagrams to visualize the relationships. Note that "Only a few land is peak" implies that "Some land is peak" and "Some land is not peak".
Step 2: Detailed Explanation:
Let's represent the statements with Venn diagrams.
From Statement 1 (Some hill is land): The circle for 'hill' and the circle for 'land' overlap.
From Statement 2 (All land is plateau): The entire 'land' circle is inside the 'plateau' circle. This also means that the overlapping part of 'hill' and 'land' is also inside 'plateau'. So, we can deduce that "Some hill is plateau".
From Statement 3 (Only a few land is peak): The 'peak' circle overlaps with the 'land' circle. This means there is an intersection between 'peak' and 'land'.
From Statement 4 (Some peak is valley): The 'peak' circle overlaps with a 'valley' circle. This statement doesn't involve 'hill', so it is less relevant for our conclusions.
Now let's evaluate the conclusions based on the relationship between 'hill' and 'peak'.
We know "Some hill is land" and "Some land is peak". The common term is 'land'. However, the part of 'land' that is 'hill' might be completely separate from the part of 'land' that is 'peak'.
Consider two possibilities:
Possibility 1: The 'peak' circle overlaps with the 'hill' circle within the 'land' area. In this case, "Some peak is hill" (Conclusion I) would be true.
Possibility 2: The 'peak' circle overlaps with 'land' but does not overlap with the 'hill' circle at all. In this case, "No hill is peak" (Conclusion II) would be true.
Since both possibilities can exist based on the given statements, we cannot definitively say that either Conclusion I is true or Conclusion II is true. However, these two conclusions form a complementary pair. One of them must be true. Either there is some overlap between hill and peak, or there is no overlap at all.
Step 3: Final Answer:
Because Conclusion I and Conclusion II are contradictory and cover all possibilities, and we cannot be certain about either one individually, the correct answer is that either conclusion I or II follows.