CCTST Deductive Reasoning 3 — Questions and Answers
Question 1: Some cats are black. All black animals are visible at night with special goggles. Which statement must be true?
- All cats are visible at night with special goggles
- Some cats are visible at night with special goggles (Correct answer)
- No cats are visible at night
- All animals visible at night are cats
Correct 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.
Question 2: 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?
- Darnell must take the final
- Darnell earns a B
- Darnell is exempt from the final (Correct answer)
- We cannot determine Darnell's exam status
Correct 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.
Question 3: All squares are rectangles. Figure X is not a rectangle. What can be concluded about Figure X?
- Figure X is a square
- Figure X is not a square (Correct answer)
- Figure X is a triangle
- Figure X might be a square
Correct answer: Figure X is not a square
Since being a rectangle is necessary for being a square, a non-rectangle cannot be a square.
Question 4: No professors are undergraduates. Some students are undergraduates. What must be true?
- Some students are professors
- Some students are not professors (Correct answer)
- All professors are students
- No students are professors
Correct answer: Some students are not professors
The undergraduates among students cannot be professors, so at least some students are not professors.
Question 5: If the hypothesis is false, the experiment is invalid. The experiment is valid. What follows?
- The hypothesis is false
- The hypothesis is true (Correct answer)
- The experiment proves the hypothesis
- Nothing can be concluded about the hypothesis
Correct answer: The hypothesis is true
By modus tollens, a valid experiment (not invalid) implies the hypothesis is not false (i.e., true).
Question 6: All prime numbers greater than 2 are odd. 7 is a prime number greater than 2. Therefore:
- 7 is even
- 7 is odd (Correct answer)
- 7 is composite
- 7 is not a prime
Correct answer: 7 is odd
Direct application of modus ponens: 7 fits the antecedent, so the consequent (odd) must hold.
Question 7: Either the report is late or it was submitted electronically. The report is not late. Which conclusion follows?
- The report was not submitted
- The report was submitted electronically (Correct answer)
- The report will be late next time
- The report was submitted by mail
Correct answer: The report was submitted electronically
Disjunctive syllogism eliminates 'late,' leaving 'submitted electronically' as the only option.
CCTST Deductive Reasoning 3
Some cats are black.
All black animals are visible at night with special goggles.
Which statement must be true?