In each of the questions below are given a few statements followed by two…

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In each of the questions below are given a few statements followed by two conclusions. Take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follow(s) from the given statements, disregarding commonly known facts.

Statements:

  • All apples are bananas.

  • No banana is a mango.

  • Some mangoes are oranges.

Conclusions:

  • I. All oranges can never be bananas.

  • II. Some mangoes are apples.

  1. A.

    Only conclusion I follows

  2. B.

    Only conclusion II follows

  3. C.

    Either conclusion I or conclusion II follows.

  4. D.

    Neither conclusion I nor conclusion II follows.

Attempted by 2 students.

Show answer & explanation

Correct answer: A

Concept: In syllogisms, convert each statement into a set relation — "All A are B" means A is fully inside B; "No A is B" means A and B share no member; "Some A are B" means A and B overlap by at least one member. A conclusion is valid only if it holds in every diagram consistent with all the statements, not just in one possible arrangement.

Application:

  1. Translate the statements: apples are fully inside bananas; bananas and mangoes share no member; mangoes and oranges overlap by at least one member.

  2. Since bananas and mangoes never overlap, the part of mangoes that overlaps oranges can never be banana. So that overlapping slice of oranges is guaranteed to be non-banana — meaning oranges can never be entirely inside bananas. This makes Conclusion I necessarily true.

  3. Since apples are fully inside bananas, and bananas share no member with mangoes, apples cannot share any member with mangoes either. So no mango can be an apple in any valid diagram, and Conclusion II does not follow.

Cross-check: Even in the most favourable arrangement for Conclusion II — where the mango–orange overlap is made as large as possible — that overlap still cannot include any banana, and apples never leave the banana region, so apples and mangoes stay separated in every valid diagram. This confirms Conclusion I always holds and Conclusion II never does, across every arrangement consistent with the statements.

Result: Only Conclusion I follows.

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