Deductive Reasoning Flashcards

Some cats are black. All black animals are visible at night with special goggles. Which statement must be true?

Answer: Some cats are visible at night with special goggles

The black cats (a subset of cats) are all visible at night, so some cats must be visible.

If you score above 90, you earn an A. If you earn an A, you are exempt from the final. Darnell scored 95. What follows?

Answer: Darnell is exempt from the final

95 > 90 triggers the first rule (A grade), which triggers the second rule (final exemption) via chained modus ponens.

All squares are rectangles. Figure X is not a rectangle. What can be concluded about Figure X?

Answer: Figure X is not a square

Since being a rectangle is necessary for being a square, a non-rectangle cannot be a square.

No professors are undergraduates. Some students are undergraduates. What must be true?

Answer: Some students are not professors

The undergraduates among students cannot be professors, so at least some students are not professors.

If the hypothesis is false, the experiment is invalid. The experiment is valid. What follows?

Answer: The hypothesis is true

By modus tollens, a valid experiment (not invalid) implies the hypothesis is not false (i.e., true).

All prime numbers greater than 2 are odd. 7 is a prime number greater than 2. Therefore:

Answer: 7 is odd

Direct application of modus ponens: 7 fits the antecedent, so the consequent (odd) must hold.

Either the report is late or it was submitted electronically. The report is not late. Which conclusion follows?

Answer: The report was submitted electronically

Disjunctive syllogism eliminates 'late,' leaving 'submitted electronically' as the only option.