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LearnLogical ReasoningCritical Reasoning

11.01 · Critical Reasoning

Syllogisms

Open lesson10 rules10 questions

On the syllabus of

Rules

At a glance 10 rules

  1. 1Statements are trueTake every statement as true, even if it sounds absurd, and add nothing. A conclusion follows only if no diagram the statements allow can break it.
  2. 2Every group has membersEach group named in a statement has at least one member, so 'All A are B' also gives 'Some A are B' and 'Some B are A'.
  3. 3Turning a statement around'Some A are B' and 'No A is B' turn around freely. 'All A are B' turns only into 'Some B are A', and 'Some A are not B' never turns around.
  4. 4Chaining 'All'Link through the shared middle term: All A are B + All B are C gives All A are C; All A are B + No B is C gives No A is C.
  5. 5Chaining 'Some'Some A are B + All B are C gives Some A are C. Some A are B + No B is C gives Some A are not C, never 'No A is C'.
  6. 6No followed by AllNo A is B + All B are C gives only Some C are not A. 'No A is C' fails: A can still share members with the part of C outside B.
  7. 7One group, two 'All'All A are B + All A are C gives Some B are C, because the members of A sit in both groups.
  8. 8No definite linkSome + Some, All A are B + Some B are C, All A are B + All C are B, and No + No give no definite link between the two end terms.
  9. 9Positive in, positive outIf every statement is an 'All' or a 'Some', no definite 'No' or 'Some ... not' conclusion can follow.
  10. 10Possibility'Some A being B is a possibility' follows if one allowed diagram shows it. A given or derived 'No' (or 'Some ... not' against an 'All') rules it out.

Test yourself

10 questions · 3 easy · 4 medium · 3 hard

Tap an option to answer. The first tap counts.

  1. Q1Easy

    Take the statements as true, even if they seem odd.

    Statements:

    All kites are parrots.

    All parrots are trains.

    Conclusions:

    I. All trains are kites.

    II. All kites are trains.

    Which conclusion(s) follow?

    Correct answerOnly II follows

    Why

    All + All chains in one direction only: kite to parrot to train.

    So every kite is a train, but 'All trains are kites' runs the chain backwards, and an 'All' never turns around.

    So only conclusion II follows.

  2. Q2Easy

    Consider the two statements “Some apps are games” and “All games are free.” Which of the following conclusions can be drawn from them?

    I. Some apps are free.

    II. All free things are games.

    Correct answerI only

    Why

    Some + All gives Some: the apps that are games all land inside the free group.

    That gives I, while II flips 'All games are free' backwards, and an 'All' cannot be flipped.

    So I follows and II does not.

8 more questions: 1 easy, 4 medium, 3 hard

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