Two statements are given below followed by two conclusions numbered as I and…

2024

Two statements are given below followed by two conclusions numbered as I and II respectively. Consider the given statements as true even if they seem to be not. After reading all the conclusions, confirm which of the given conclusions logically follows, disregarding commonly known facts.

Statements:

I. All jeeps are cars.

II. Some cars are Hondas.

Conclusions:

I. Some Hondas are cars.

II. No jeep is a Honda.

  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.

Show answer & explanation

Correct answer: A

Concept

Two syllogism rules govern this pair of statements: (1) A particular affirmative statement of the form "Some B are C" converts validly to "Some C are B" — this immediate inference (conversion) always holds by itself. (2) A conclusion connecting the two end terms of two statements is valid only if their common middle term is distributed (refers to the WHOLE of that class) in at least one statement; if the middle term is undistributed in both, no relationship between the end terms can be validly concluded (the fallacy of the undistributed middle).

Application

  1. Statement I, "All jeeps are cars," is a universal affirmative (A-type); its predicate "cars" is undistributed.

  2. Statement II, "Some cars are Hondas," is a particular affirmative (I-type); its subject "cars" is also undistributed.

  3. Since "cars," the middle term common to both statements, is undistributed in each, rule (2) blocks any valid conclusion linking jeeps and Hondas directly.

  4. Applying rule (1) to Statement II alone: "Some cars are Hondas" converts directly to "Some Hondas are cars."

Cross-check

Picture the three classes as circles: one valid arrangement has the jeeps-circle and Hondas-circle fully disjoint, another has them overlapping — both remain consistent with the two given statements, confirming no fixed relationship between jeeps and Hondas can be concluded either way. By contrast, every arrangement satisfying "Some cars are Hondas" automatically also satisfies "Some Hondas are cars," since an overlap read from either direction describes the same region — confirming this conclusion cannot fail.

Result: exactly one of the two given conclusions is validly derivable from the statements.

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