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Syllogisms and Deductions Flashcards

6 cards from real CCAT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. If A > B and B > C, which of the following must be true?

    Answer: A > C

    By transitivity of inequality: A > B and B > C implies A > C.

  2. Premises: All X are Y. No Z are Y. Conclusion: No X are Z. Is this valid?

    Answer: Valid

    X is inside Y. Z has no overlap with Y. Since X is entirely in Y, and Z has no overlap with Y, X and Z cannot overlap.

  3. Premises: Either the meeting is on Monday or Tuesday. The meeting is not on Monday. Conclusion: The meeting is on Tuesday.

    Answer: Valid — disjunctive syllogism

    Disjunctive syllogism: (P or Q); not P; therefore Q. Valid form.

  4. Premises: If Maria studies, she passes. Maria did not pass. Conclusion: Maria did not study.

    Answer: Valid — modus tollens

    Modus tollens: If P then Q; not Q; therefore not P. Studies implies passes; did not pass; therefore did not study.

  5. Premises: All squares are rectangles. Shape X is not a rectangle. Conclusion: Shape X is not a square.

    Answer: Valid

    Contrapositive: not-rectangle implies not-square. Shape X is not a rectangle, so it cannot be a square.

  6. Premises: Some students are athletes. Some athletes are musicians. Conclusion: Some students are musicians. Is this valid?

    Answer: Invalid

    Invalid. The students who are athletes and the athletes who are musicians could be completely different people.