Difficulty: Medium
Correct Answer: Only conclusion (I) follows
Explanation:
Introduction / Context:
This question belongs to the standard syllogism type where you must reason about set relationships involving banks, private entities, and industry. The statements are to be taken as logically true, and your task is to check which conclusions must hold in every possible interpretation that respects these statements. It is essential to distinguish between definite conclusions and overgeneralizations.
Given Data / Assumptions:
Concept / Approach:
The phrase “Some banks are private” indicates there is at least one bank that belongs to the subset of private entities. The second statement, “All private are industry,” means that the set of private entities is completely contained within the set of industry. We can chain these ideas: if some banks are private and all private are industry, then those particular banks are also part of industry. This directly supports a “some” type conclusion. However, we must be careful not to overextend this to “all banks.”
Step-by-Step Solution:
Step 1: Represent the set of industry as a large circle.Step 2: Place the private set completely inside the industry set, because all private are industry.Step 3: Place the banks set such that it overlaps the private region in at least one area, because some banks are private. It may have additional parts outside the private region, about which we know nothing.Step 4: Check conclusion (I): “Some banks are industry.” The banks that lie in the private region are also in industry, since private is inside industry. Therefore, there is at least one bank that belongs to industry. So conclusion (I) must be true in every valid diagram.Step 5: Check conclusion (II): “All banks are industry.” This would require the entire banks set to lie completely inside the industry set. The original statements, however, only restrict the private part of banks. They do not say that all banks are private or that banks have no part outside the private or industry regions. It is possible that some banks lie outside the industry set, which would still satisfy the statements. So conclusion (II) does not necessarily follow.
Verification / Alternative check:
Symbolically, we can express the logic as follows. From statement (I), there exists at least one object x such that x is a bank and x is private. From statement (II), for any object y, if y is private then y is industry. Combining these, for that object x, x is bank, x is private, and x is industry. Thus, there exists at least one bank that is industry, which confirms conclusion (I). However, the statements never assert that for every bank z, z is industry, so conclusion (II) cannot be guaranteed.
Why Other Options Are Wrong:
Option B claims that only conclusion (II) follows, ignoring the fact that (II) goes beyond the information given. Option C suggests that neither conclusion follows, which is incorrect because we have a clear chain proving conclusion (I). Option D states that both conclusions follow, but this overstates what the statements support by including the unjustified universal claim in conclusion (II). Only option A, which accepts conclusion (I) and rejects conclusion (II), aligns with rigorous logical analysis.
Common Pitfalls:
Students sometimes misread “Some banks are private” as “All banks are private,” which leads them to conclude “All banks are industry.” This is a classic error of replacing “some” with “all.” Another common mistake is to think that if part of a set is inside a larger set, then the whole set must also be inside, which is not true. Always pay close attention to quantifiers like “some” and “all,” as they significantly change the meaning of statements.
Final Answer:
Thus, the correct conclusion is that only conclusion (I) follows from the given statements.
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