Two statements are given followed by four conclusions I, II, III and IV. You…

2020

Two statements are given followed by four conclusions I, II, III and IV. You have to consider these statements to be true, even if they seem at variance from commonly known facts. Decide which of the given conclusions logically follow/s from the given statement.

Statements:

  1. All judges are lawyers.

  2. Some lawyers are seniors.

Conclusions: I. Some seniors are judges. II. Some seniors are lawyers. III. Some lawyers are judges. IV. Some judges are seniors.

  1. A.

    Only conclusions I and IV follow

  2. B.

    Only conclusions III and IV follow

  3. C.

    Only conclusions I and II follow

  4. D.

    Only conclusions II and III follow

Attempted by 2 students.

Show answer & explanation

Correct answer: D

Concept: Two rules of immediate inference decide which conclusions validly follow from two categorical statements.

  • A particular statement ("some A are B") converts simply to "some B are A" -- no information is lost.

  • A universal statement ("all A are B") converts by limitation to "some B are A", valid once the subject class A is taken to be non-empty (the standard assumption in these questions).

  • No conclusion may validly link two classes unless the class shared between the statements (the middle term) is distributed -- used as the subject of a universal statement -- in at least one of them; appearing only as a predicate, or as the subject of a "some" statement in both places, is not enough (the undistributed-middle fallacy).

Application: Statement 1, "All judges are lawyers", is universal with judges as the distributed subject; statement 2, "Some lawyers are seniors", is particular with lawyers as its (undistributed) subject.

  1. Convert statement 1 by limitation (judges non-empty): "All judges are lawyers" gives "Some lawyers are judges" -- this is exactly conclusion III.

  2. Convert statement 2 simply: "Some lawyers are seniors" gives "Some seniors are lawyers" -- this is exactly conclusion II.

  3. Lawyers is the predicate of the universal statement and the subject of the particular statement -- undistributed in both -- so no statement distributes lawyers, and no valid judges-seniors relationship can be drawn in either direction. Conclusions I and IV therefore do not follow.

Cross-check: Draw the judges circle wholly inside the lawyers circle (per statement 1), then draw the seniors circle overlapping lawyers only in a region placed entirely outside the judges circle (statement 2 only requires some lawyer-senior overlap, not that it touch the judges subset). This diagram satisfies both statements while making I and IV false, and no diagram consistent with the statements can make II or III false, confirming the split.

Result: Only conclusions II and III follow, matching "Only conclusions II and III follow."

Why the other combinations fall short:

  • "Only conclusions I and IV follow" chains the two statements straight through to a judges-seniors claim, ignoring that lawyers is undistributed in both statements.

  • "Only conclusions III and IV follow" keeps the valid judges-lawyers restatement but adds the unsupported judges-seniors claim.

  • "Only conclusions I and II follow" keeps the valid lawyers-seniors restatement but adds the unsupported judges-seniors claim.

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