Two statements are given below, followed by two conclusions numbered I and II.…

2023

Two statements are given below, followed by two conclusions numbered I and II. Consider the given statements to be true, even if they seem to vary from commonly known facts. After reading the conclusions, decide which of them logically follows, disregarding commonly known facts.

Statements:

I. Some eyes are heads.

II. Some ears are heads.

Conclusions:

I. All eyes are ears.

II. At least some heads are not ears.

  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: D

Concept: In syllogisms, an I-type premise ('Some A are B') distributes neither its subject nor its predicate term, and a valid conclusion joining two end terms requires the shared middle term to be distributed in at least one premise. Two particular (I-type) premises sharing an undistributed middle term therefore never yield a valid conclusion between their end terms - the classical 'I + I = No conclusion' rule. Separately, the simple conversion of an I-type statement ('Some A are B') validly yields only another I-type statement ('Some B are A'); it can never yield a negative (O-type) statement.

  1. Premise I, 'Some eyes are heads', is an I-type statement with the middle term 'heads' as its predicate (undistributed).

  2. Premise II, 'Some ears are heads', is also I-type, with 'heads' again as its (undistributed) predicate.

  3. Since the middle term 'heads' is undistributed in both premises, they cannot be combined into any valid conclusion linking eyes and ears - so 'All eyes are ears' is not established, let alone as a universal claim (two particular premises never license a universal conclusion).

  4. Converting premise II alone gives 'Some heads are ears' (I-type) - a positive, existential relation between heads and ears.

  5. 'At least some heads are not ears' is an O-type (negative) statement; it can never follow from an I-type premise or its valid conversion.

Cross-check: Both conclusions fail for the same underlying reason - the premises supply only positive, particular information tied together by an undistributed middle term, which is structurally incapable of yielding either a universal claim (eyes-ears) or a negative claim (heads-ears). Hence neither conclusion I nor conclusion II follows; the correct choice is 'If neither conclusion I nor II follows.'

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