Deductive Reasoning Flashcards

All birds have wings. Penguins are birds. Which statement must be true?

Answer: Penguins have wings

Universal syllogism: penguins belong to the class birds, so they inherit the property of having wings.

If a shape has four equal sides and four right angles, it is a square. Shape Q has four equal sides but its angles are not all right angles. What follows?

Answer: Shape Q is not a square

Both conditions (equal sides AND right angles) are required; missing one is sufficient to conclude Shape Q is not a square.

No valid argument has a false conclusion when its premises are true. Argument Z has true premises and a false conclusion. What follows?

Answer: Argument Z is not valid

The definition directly excludes Argument Z: true premises with a false conclusion = invalid.

All lawyers passed the bar exam. Some bar exam passers work in tech. What must be true?

Answer: Nothing certain can be said about lawyers in tech

The 'some' who work in tech may or may not overlap with the lawyers subset; no conclusion is forced.

If you are a citizen, you may vote. If you may vote, you can influence elections. Carlos is a citizen. What follows?

Answer: Carlos can influence elections

Chained modus ponens: citizen → may vote → can influence elections, and Carlos is a citizen.

No herbivores eat meat. A wolf eats meat. What must be true about the wolf?

Answer: The wolf is not a herbivore

Because herbivores never eat meat and the wolf does, the wolf cannot be a herbivore.

All employees must wear badges. Everyone wearing a badge has access to the building. Which conclusion is valid?

Answer: All employees have access to the building

Employees → badges → building access; chaining gives all employees access to the building.