Suppose that each of the following statements is true:
- If mongoes eat booms, then mongoes are dangerous.
- Either flems are tall or mongoes are not dangerous.
- Flems are not tall.
Which of the following conclusions must also be true?
- Mongoes eat booms.
- Mongoes do not eat booms.
- Flems are not dangerous.
- Mongoes are dangerous.
- None of these statements must also be true.
Solution
Look at the third statement: Flems are not tall. This tells us, from the second statement, that mongoes are not dangerous. Thus, according to the first statement and taking its contrapositive, mongoes do not eat booms. This is conclusion B. Contrapositives are lovely.