In each question below some statements are given followed by two conclusions…

2022

In each question below some statements are given followed by two conclusions numbered I and II. You have to 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 follows from the given statements, disregarding commonly known facts. Give answer

Statements:
Some A are B.
All C are D.
No B is C.
Conclusions:
I. Some D are not B.
II. Some D are B.

  1. A.

    If only conclusion I follows.

  2. B.

    If only conclusion II follows.

  3. C.

    If either conclusion I or II follows.

  4. D.

    If neither conclusion I nor II follows.

  5. E.

    If both conclusions I and II follow.

Attempted by 4 students.

Show answer & explanation

Correct answer: A

Concept

In syllogism, a conclusion 'follows' only if it is true in EVERY arrangement (Venn diagram) consistent with the statements. Two governing rules apply here: (1) a universal affirmative 'All C are D' has existential import — it asserts that the class C actually exists, so at least one D is a C; (2) 'No B is C' means the sets B and C are completely separate. A merely possible relationship is NOT a valid conclusion; only a forced one is.

Application

  1. From 'All C are D', every C lies inside D, and since C is a non-empty class, at least one member of D is in fact a C.

  2. From 'No B is C', that C (which is a D) cannot be a B. Hence at least one D is not B — Conclusion I, 'Some D are not B', is forced and always true.

  3. For Conclusion II, 'Some D are B': the only B we know about come from 'Some A are B'. Nothing ties those B to D. We can draw a valid diagram where the A-B overlap sits entirely outside D, so no D is B. Therefore II is only possible, not necessary.

Cross-check

Test the 'either-or' trap: I and II are NOT a complementary pair here, because Conclusion I is already definitely true on its own. An 'either/or' verdict requires that neither is individually certain while one of them must hold — that condition fails. Likewise 'both follow' fails because II can be made false, and 'neither follows' fails because I is forced.

Result

Only Conclusion I definitely follows, so the correct response is 'If only conclusion I follows.'

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