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GATE 2023 EC GA Q.6: solution and answer

GATE 2023 · ECGA Q.6 · 2 marks · MCQ

Forestland is a planet inhabited by different kinds of creatures. Among other creatures, it is populated by animals all of whom are ferocious. There are also creatures that have claws, and some that do not. All creatures that have claws are ferocious.

Based only on the information provided above, which one of the following options can be logically inferred with certainty?

  1. (A)

    All creatures with claws are animals.

  2. (B)

    Some creatures with claws are non-ferocious.

  3. (C)

    Some non-ferocious creatures have claws.

  4. (D)

    Some ferocious creatures are creatures with claws.

See the question in the paper
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Answer and solution

ANSWER

Only option (D), "Some ferocious creatures are creatures with claws.", can be inferred with certainty.

Official answer: DSource: Official answer key, GATE 2023 EC (IIT Kanpur)

  1. Write the facts as statements. (1) All animals are ferocious. (2) Creatures with claws exist, and so do creatures without claws. (3) All creatures that have claws are ferocious.

  2. Draw it as sets. The set of animals lies inside the set of ferocious creatures, and so does the set of clawed creatures. Nothing is said about how animals and clawed creatures overlap.

  3. (A) is not certain. Animals and clawed creatures both lie inside the ferocious set, but two subsets of one set can be disjoint, can overlap, or one can contain the other. Sharing the property 'ferocious' does not make a clawed creature an animal. This is the fallacy of the undistributed middle.

  4. (B) is false. 'All creatures with claws are ferocious' and 'Some creatures with claws are non-ferocious' are contradictories: if one is true, the other must be false. Statement (3) is given as true, so (B) is false.

  5. (C) is false for the same reason. 'Some non-ferocious creatures have claws' says the same thing as (B), because 'Some X are Y' and 'Some Y are X' are equivalent. Statement (3) rules it out.

  6. (D) is certain. By statement (2), at least one clawed creature exists, and by statement (3) it is ferocious. That creature is both ferocious and clawed, so 'Some ferocious creatures are creatures with claws' follows. This converts 'All C are F' into 'Some F are C', which is valid only because the clawed set is known to be non-empty.

  7. Only (D) follows with certainty.

KEY IDEA

From 'All C are F' you can infer 'Some F are C' only if at least one C exists. The stem gives that directly ("There are also creatures that have claws"), so option (D) is guaranteed. Being inside the same larger set (ferocious) says nothing about how animals and clawed creatures relate to each other.

WATCH OUT FOR

Choosing (A) by reasoning 'animals are ferocious and clawed creatures are ferocious, so clawed creatures are animals'. That is the undistributed middle, because two groups that share a property need not overlap. A second trap is rejecting (D) on the grounds that a universal statement does not prove anything exists. The stem states outright that clawed creatures exist, so the existence condition is met.

From the GATE 2023 EC paper. Every question of this paper · Download the full paper · All 41 Reasoning questions, with notes

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