Deductive Reasoning Flashcards

All managers are employees. Some employees are remote workers. Which conclusion must be true?

Answer: Some managers may be remote workers

Since only 'some' employees are remote workers, managers (a subset of employees) may or may not be among those remote workers, making it possible but not certain.

If it rains, the ground gets wet. The ground is wet. What can we conclude?

Answer: It might have rained, or something else caused it

A wet ground is consistent with rain but could have other causes; we cannot confirm rain was the reason from the wet ground alone.

No birds are mammals. All penguins are birds. Which statement must be true?

Answer: No penguins are mammals

Since all penguins are birds and no birds are mammals, it follows necessarily that no penguins are mammals.

Every team that trains daily wins competitions. Team A does not win competitions. What can be deduced?

Answer: Team A does not train daily

By contrapositive logic, if not winning implies not training daily, then Team A does not train daily.

Some students passed the exam. All students who passed the exam received a certificate. Which must be true?

Answer: Some students received a certificate

Since some students passed and all who passed got certificates, at least those students received certificates, making 'some students received a certificate' necessarily true.

If a number is divisible by 6, it is divisible by both 2 and 3. The number 18 is divisible by 6. What can be concluded?

Answer: 18 is divisible by both 2 and 3

Applying the given rule directly: since 18 is divisible by 6, it must be divisible by both 2 and 3.

All red cards in the deck are hearts or diamonds. This card is a club. What must be true?

Answer: This card is not red

Clubs are neither hearts nor diamonds; since red cards must be hearts or diamonds, a club cannot be red.