Direction: In the question below are given three statements followed by two…

2024

Direction: In the question below are given three statements 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.

Statements:

I. All metals are plastics

II. No plastic is ore

III. Only a few ores are wood

Conclusions:

I. All plastic is wood

II. Some plastics are not wood

  1. A.

    Only conclusion I follows

  2. B.

    Either conclusion I or II follows

  3. C.

    Only conclusion II follows

  4. D.

    Neither conclusion I nor II follows

Attempted by 13 students.

Show answer & explanation

Correct answer: B

Concept

When two given conclusions share the same subject and predicate but are worded as exact logical opposites - ‘All A is B’ against ‘Some A is not B’ - they form a complementary pair: one of the two is always true and both can never be false together. If checking each conclusion on its own shows that neither is forced by the statements, the correct call is that one of them - either the first or the second - follows, rather than neither and rather than picking just one as the sole answer.

Application

  1. Statement II (‘No plastic is ore’) keeps the plastic group and the ore group completely separate from each other.

  2. Statement III (‘Only a few ores are wood’) means some ore is wood and some ore is not wood. Statement I (‘All metals are plastics’) never mentions wood at all, so it has no bearing on how plastic and wood relate.

  3. None of the three statements fixes how the plastic group and the wood group relate to each other directly, so try both admissible arrangements: (a) place the whole plastic group inside the wood group, and (b) place the plastic group and the wood group with no overlap at all.

  4. Both arrangements still satisfy statement II (plastic and ore stay separate in both) and statement III (ore and wood can still overlap partially in both). So both are valid pictures of the given statements.

  5. In arrangement (a), ‘All plastic is wood’ holds and ‘Some plastics are not wood’ fails. In arrangement (b), ‘Some plastics are not wood’ holds and ‘All plastic is wood’ fails. So neither conclusion is guaranteed by itself.

  6. But the two conclusions are exact opposites about the very same subject (plastic) and predicate (wood), so across every admissible arrangement exactly one of them is always true. That makes ‘Either conclusion I or II follows’ the outcome that always holds.

Cross-check

Take Metals = {a}, Plastic = {a, b}, Ore = {c, d}, Wood = {a, b, c}: every metal (a) is plastic, so statement I holds; plastic and ore share nothing, so statement II holds; ore and wood share only c (d is ore but not wood), so ‘only a few ores are wood’ also holds; and every plastic item (a and b) is wood, so ‘All plastic is wood’ is true here. Now take Metals = {a}, Plastic = {a, b}, Ore = {d, e}, Wood = {c, d}: statement I still holds (a is plastic); plastic and ore again share nothing, and ore and wood share only d (e is ore but not wood), so statement III still holds - but no plastic item is wood, so ‘Some plastics are not wood’ is true here instead. Both sets obey every given statement, yet each time a different one of the two conclusions turns out true, confirming the either-or result.

Result

So only conclusion I or conclusion II follows - not conclusion I alone, not conclusion II alone, and not neither.

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