Difficulty: Easy
Correct Answer: Only conclusion II follows
Explanation:
Introduction / Context:
This question is a classic example of syllogism based reasoning used in many competitive exams. You are given two statements about mangoes, golden colour, and cheapness, and then two possible conclusions. The task is to see which conclusion must follow logically if both statements are accepted as absolutely true. Real life knowledge about mangoes or prices is irrelevant; only the internal logic matters.
Given Data / Assumptions:
Concept / Approach:
The first statement tells us that the set of mangoes is fully contained inside the set of golden coloured things. The second statement tells us that there is no overlap between golden coloured things and cheap things. In set language, golden things and cheap things are disjoint. To decide which conclusion follows, we combine these two relations carefully. A conclusion follows only when it must be true in every diagram that satisfies both statements.
Step-by-Step Solution:
Step 1: Represent the set of golden coloured things as a large circle.Step 2: Draw the set of mangoes as a smaller circle completely inside the golden circle, because every mango is golden.Step 3: Represent the set of cheap things as another circle that does not intersect the golden circle at all, since no golden thing is cheap.Step 4: Consider conclusion I: “All mangoes are cheap.” This would require the mangoes circle to be completely contained in the cheap circle. But our diagram shows that mangoes are inside the golden region and golden things do not intersect cheap things at all. So mangoes cannot be cheap. Conclusion I directly contradicts the combined effect of the statements, so it cannot follow.Step 5: Consider conclusion II: “Golden coloured mangoes are not cheap.” Every mango is golden, and every golden thing is not cheap. So if we talk about golden coloured mangoes, they must also be not cheap. This conclusion simply restates the logical consequence of the two statements and therefore follows.
Verification / Alternative check:
We can also reason symbolically. From statement 1, mango implies golden. From statement 2, golden implies not cheap. By linking these, mango implies not cheap. Therefore, any mango cannot be cheap. Conclusion II talks exactly about golden coloured mangoes being not cheap, which agrees with this chain. Conclusion I, on the other hand, says the opposite. It would require mango implies cheap, which contradicts mango implies not cheap. Hence only conclusion II is logically valid.
Why Other Options Are Wrong:
Option A, which claims only conclusion I follows, is wrong because conclusion I conflicts with the second statement. Option C, which suggests that either conclusion I or conclusion II follows, is wrong since they are not both possible logical consequences; only the second can be correct. Option D claims that both follow, which is impossible because they say opposite things about the same set of mangoes. Only option B, supporting conclusion II alone, matches the derived logic.
Common Pitfalls:
A common mistake is to misread the second statement and think that no cheap thing is golden, then confuse the direction and assume that no golden thing is cheap means nothing else can be cheap either. Another error is to ignore the word “no” and accidentally treat golden items as possibly cheap. Always track the direction of implications and the presence of negative words like “no” and “not.” Drawing a clear Venn diagram usually prevents such confusion.
Final Answer:
Therefore, the correct reasoning shows that only conclusion II follows from the given statements.
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