Syllogisms

All cats are animals. All animals need food. Therefore, which statement must be true?

• AOnly cats need food
• BSome animals do not need food
• CAll cats need food✓
• DAll animals are cats

Answer: Since all cats are animals and all animals need food, it follows that all cats need food.

All roses are flowers. All flowers are plants. Therefore, which statement must be true?

• AAll roses are plants✓
• BNo flowers are plants
• CSome roses are not plants
• DAll plants are roses

Answer: Chaining the two statements, all roses are flowers and all flowers are plants, so all roses are plants.

No fish can fly. All trout are fish. Therefore, which statement must be true?

• ASome fish are trout that fly
• BNo trout can fly✓
• CAll flying things are fish
• DSome trout can fly

Answer: If no fish can fly and all trout are fish, then no trout can fly.

All doctors are graduates. Some graduates are wealthy. Which conclusion is valid?

• ANo doctors at all are wealthy people
• BNo valid conclusion about doctors being wealthy can be drawn✓
• CSome doctors are wealthy
• DAll doctors are wealthy

Answer: Knowing some graduates are wealthy does not tell us whether any of those wealthy graduates are doctors, so no conclusion about doctors being wealthy follows.

All squares are rectangles. All rectangles have four sides. Therefore, which must be true?

• AAll four-sided shapes are squares
• BNo rectangles are squares
• CSome squares have three sides
• DAll squares have four sides✓

Answer: Since all squares are rectangles and all rectangles have four sides, all squares have four sides.

Some birds cannot fly. All penguins are birds. Which statement must be true?

• ASome birds cannot fly✓
• BPenguins are not birds
• CAll birds are penguins
• DSome penguins cannot fly

Answer: The first premise is given as true, so it must still hold. The second premise puts every penguin inside the set of birds but does not say which birds are the flightless ones, so nothing follows about whether any penguin can fly; real-world knowledge about penguins is not one of the premises. Reversing the second premise is an invalid conversion, and denying that penguins are birds contradicts it.

All managers attend the meeting. John attends the meeting. Which conclusion is valid?

• AAll meeting attendees are managers
• BJohn is a manager
• CJohn is not a manager
• DWe cannot conclude John is a manager✓

Answer: Attending the meeting does not make someone a manager; non-managers might also attend, so we cannot conclude John is a manager.

No reptiles are mammals. All snakes are reptiles. Therefore, which must be true?

• AAll mammals are snakes
• BSome reptiles are mammals
• CSome snakes are mammals
• DNo snakes are mammals✓

Answer: If no reptiles are mammals and all snakes are reptiles, then no snakes are mammals.

All teachers are patient. Maria is patient. Which conclusion is valid?

• AAll patient people are teachers
• BWe cannot conclude Maria is a teacher✓
• CMaria is not patient
• DMaria is a teacher

Answer: Being patient does not mean being a teacher, since other people can be patient too, so we cannot conclude Maria is a teacher.

Some students study French. All who study French can read it. Which statement must be true?

• ASome students can read French✓
• BAll students can read French
• CNo students can read French
• DOnly French students exist

Answer: Since some students study French and all French students can read it, at least some students can read French.

All A are B. No B are C. Therefore, which must be true?

• ANo A are C✓
• BAll A are C
• CSome A are C
• DAll C are A

Answer: If all A are B and no B are C, then no A can be C.

All metals conduct electricity. Copper is a metal. Therefore, which must be true?

• AOnly copper conducts electricity
• BAll conductors are copper
• CCopper does not conduct electricity
• DCopper conducts electricity✓

Answer: Since all metals conduct electricity and copper is a metal, copper conducts electricity.

Some employees work weekends. All who work weekends get extra pay. Which statement must be true?

• AAll employees get extra pay
• BOnly weekend workers are employees
• CNo employees get extra pay
• DSome employees get extra pay✓

Answer: Since some employees work weekends and weekend workers get extra pay, at least some employees get extra pay.

All dogs bark. Some pets are dogs. Therefore, which must be true?

• ANo pets bark
• BAll barking things are pets
• CSome pets bark✓
• DAll pets bark

Answer: Since some pets are dogs and all dogs bark, some pets bark.

No cars are bicycles. Some vehicles are cars. Which conclusion is valid?

• AAll cars are vehicles only
• BNo vehicles exist
• CAll vehicles are bicycles
• DSome vehicles are not bicycles✓

Answer: Since some vehicles are cars, and no cars are bicycles, those vehicles are not bicycles, so some vehicles are not bicycles.

All members pay a fee. Sam does not pay a fee. Therefore, which must be true?

• ASam is a member
• BSam is not a member✓
• CAll non-members pay a fee
• DSam pays double

Answer: Since all members pay a fee and Sam does not, Sam cannot be a member.