Each of the questions below has a few statements, followed by four conclusions…

2023

Each of the questions below has a few statements, followed by four conclusions numbered I, II, III and IV. You have to consider every given statement as true, even if it does not conform to well known facts. Read the conclusions and then decide which of the conclusions can be logically derived.

Statements: All jugs are glasses. All glasses are cups. All jugs are pens.

  • I. All pens are jugs.

  • II. Some glasses are pens.

  • III. Some cups are pens.

  • IV. All pens are cups.

  1. A.

    None

  2. B.

    Only II and III

  3. C.

    Only II

  4. D.

    Only II and either I or III

Show answer & explanation

Correct answer: B

Concept: In categorical syllogisms, "All A are B" means the class A sits entirely inside class B, and such statements chain together (if A is inside B, and B is inside C, then A is inside C too). Whenever a single non-empty class is placed entirely inside two other classes, that alone guarantees some overlap between those two classes - a valid "Some" conclusion. No conclusion can claim more than these two rules allow.

Applying it here:

  1. "All jugs are glasses" and "All jugs are pens" place the class of jugs entirely inside both glasses and pens. Since jugs is non-empty, some element is both a glass and a pen.

  2. "All jugs are glasses" combined with "All glasses are cups" chains together: every jug is therefore also a cup.

  3. Jugs is now placed entirely inside both cups (from step 2) and pens (given). Since jugs is non-empty, some element is both a cup and a pen.

  4. These are the only two overlaps the premises license - between glasses and pens, and between cups and pens.

Checking each conclusion:

  • I claims every pen is a jug - this reverses the direction of "all jugs are pens"; a class being fully inside a second class never means the second is fully inside the first, so this is not warranted.

  • II matches exactly the overlap derived in step 1 - it is warranted.

  • III matches exactly the overlap derived in step 3 - it is warranted.

  • IV claims every pen is a cup - the premises only place the jugs-portion of pens inside cups; the rest of the pens class is left unconstrained, so this is not warranted.

So exactly conclusions II and III follow, matching "Only II and III".

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