Syllogisms

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

• AAll animals are cats
• BAll cats need food✓
• COnly cats need food
• DSome animals do not need food

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 plants are roses
• BAll roses are plants✓
• CSome roses are not plants
• DNo flowers are plants

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

• AAll doctors are wealthy
• BSome doctors are wealthy
• CNo doctors are wealthy
• DNo valid conclusion about doctors being wealthy can be drawn✓

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
• BAll squares have four sides✓
• CSome squares have three sides
• DNo rectangles are squares

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?

• AAll birds are penguins
• BPenguins are not birds
• CAt least some birds (which may include penguins) exist
• DSome birds cannot fly✓

Answer: The premise that some birds cannot fly is given and remains true; the other options either reverse or contradict the premises.

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

• AJohn is a manager
• BJohn is not a manager
• CWe cannot conclude John is a manager✓
• DAll meeting attendees are managers

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?

• ASome snakes are mammals
• BNo snakes are mammals✓
• CAll mammals are snakes
• DSome reptiles 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?

• AMaria is a teacher
• BMaria is not patient
• CWe cannot conclude Maria is a teacher✓
• DAll patient people are teachers

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?

• AAll students can read French
• BSome 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?

• AAll A are C
• BNo 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?

• ACopper does not conduct electricity
• BCopper conducts electricity✓
• COnly copper conducts electricity
• DAll conductors are copper

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