Syllogisms and Deductions Flashcards

Some politicians are lawyers. All lawyers passed the bar exam. Which of the following is definitely true?

Answer: Some politicians passed the bar exam

The politicians who are also lawyers must have passed the bar exam, so some politicians passed it.

If it rains, the ground gets wet. The ground is not wet. What can be concluded?

Answer: It did not rain

By contrapositive, if the ground is not wet, then it did not rain.

All X are Y. All Y are Z. No Z are W. Therefore:

Answer: No X are W

X → Y → Z, and since no Z are W, no X can be W.

Some birds cannot fly. All penguins are birds. Which conclusion is valid?

Answer: Penguins might or might not be able to fly

The premises do not specify whether penguins are among the birds that cannot fly, so we cannot determine their ability.

Every employee who works overtime gets a bonus. James got a bonus. What can you conclude?

Answer: James may or may not have worked overtime

The conditional only guarantees a bonus for overtime workers; bonuses could also be given for other reasons.

No introverts enjoy large crowds. Some engineers are introverts. Which statement is certainly true?

Answer: Some engineers do not enjoy large crowds

The engineer-introverts don't enjoy large crowds, so some engineers (those who are introverts) do not enjoy large crowds.

All squares are rectangles. Shape T is not a rectangle. What follows?

Answer: Shape T is not a square

By contrapositive, if something is not a rectangle, it cannot be a square.