Logical Deduction Questions

• Syllogism — combine two “some” statements with a shared middle class Statements: • Some houses are offices. • Some offices are schools. Conclusions to evaluate: I. Some schools are houses. II. Some offices are houses. III. No house is school. IV. Some schools are offices.
• Syllogism with two independent properties — horns and lights on taxis Statements: • Some taxis have horns. • Some taxis have lights. Conclusions to evaluate: I. Every taxi has either a horn or a light. II. Some taxis have neither a light nor a horn. III. Some taxis have both horns and lights. IV. No taxi has both a horn and a light.
• Syllogism — chaining universal inclusions across three classes Statements: • All fruits are vegetables. • All pens are vegetables. • All vegetables are rains. Conclusions to evaluate: I. All fruits are rains. II. All pens are rains. III. Some rains are vegetables.
• Syllogism — mixing “some”, “no”, and a universal inclusion Statements: • Some towels are brushes. • No brush is soap. • All soaps are rats. Conclusions to evaluate: I. Some rats are brushes. II. No rat is brush. III. Some towels are soaps.
• Syllogism – Determine which conclusions logically follow Statements: • Some pictures are frames. • Some frames are idols. • All idols are curtains. Conclusions to test: I. Some curtains are pictures. II. Some curtains are frames. III. Some idols are frames.
• Syllogism – Evaluate conclusions from partial overlaps Statements: • Some hills are rivers. • Some rivers are deserts. • All deserts are roads. Conclusions to test: I. Some roads are rivers. II. Some roads are hills. III. Some deserts are hills.
• Syllogism – Chain reasoning with “all” and “some” Statements: • Some saints are balls. • All balls are bats. • Some tigers are balls. Conclusions to test: I. Some bats are tigers. II. Some saints are bats. III. All bats are balls.
• Syllogism – Books, schools, and colleges (careful with shared supersets) Statements: • Some pens are books. • All schools are books. • Some colleges are schools. Conclusions to test: I. Some colleges are pens. II. Some pens are schools. III. Some colleges are books.
• Syllogism – Buses, trains, rooms, and boats (universal negatives) Statements: • All trains are buses. • No room is a bus. • All boats are rooms. Conclusions to test: I. No boat is a train. II. No bus is a boat. III. No train is a room.
• Syllogism – Multiple “some” statements about mountains (avoid unjustified negatives) Statements: • Some mountains are hillocks. • Some mountains are rivers. • Some mountains are valleys. Conclusions to test: I. All mountains are either hillocks or rivers or valleys. II. No valley is a river. III. Some rivers are valleys.
• Syllogism – Three chained “some” statements (watch for non-guaranteed transitivity) Statements: • Some blades are hammers. • Some hammers are knives. • Some knives are axes. Conclusions to test: I. Some axes are hammers. II. Some knives are blades. III. Some axes are blades.
• Syllogism – Boxes, hammers, beads, rings (pushing existence through an “all”) Statements: • Some boxes are hammers. • Some hammers are beads. • All beads are rings. Conclusions to test: I. Some rings are hammers. II. Some hammers are boxes. III. Some rings are boxes.
• Syllogism – Blankets, beds, and pillows (using a universal to confirm existence) Statements: • Some blankets are beds. • Some pillows are blankets. • All beds are pillows. Conclusions to test: I. Some blankets are pillows. II. Some pillows are beds. III. Some beds are blankets.
• Syllogism – Dolls, bottles, cars, and windows (do not assume existence from universals) Statements: • All dolls are windows. • All bottles are windows. • All cars are bottles. Conclusions to test: I. All cars are windows. II. Some cars are dolls. III. Some windows are cars.
• Syllogism — Determine which conclusion(s) logically follow from the statements Statements: All tigers are lions. No cow is a lion. Some camels are cows. Conclusions: (I) Some lions are camels. (II) No camel is a tiger. (III) Some tigers are cows.
• Syllogism — Determine which conclusion(s) logically follow Statements: All flowers are toys. Some toys are trees. Some angels are trees. Conclusions: (I) Some angels are toys. (II) Some trees are flowers. (III) Some flowers are angels.
• Syllogism — Identify the valid conclusion(s) Statements: Some rats are cats. Some cats are dogs. No dog is a cow. Conclusions: (I) No cow is a cat. (II) No dog is a rat. (III) Some cats are rats.
• Syllogism — Determine which conclusion(s) must be true Statements: All tigers are jungles. No jungle is a bird. Some birds are rains. Conclusions: (I) No rain is a jungle. (II) Some rains are jungles. (III) No bird is a tiger.
• Syllogism — Identify the necessary conclusion(s) Statements: All snakes are trees. Some trees are roads. All roads are mountains. Conclusions: (I) Some mountains are snakes. (II) Some roads are snakes. (III) Some mountains are trees.
• Syllogism — Determine which conclusion(s) follow Statements: All trees are flowers. No flower is a fruit. All branches are fruits. Conclusions: (I) Some branches are trees. (II) No fruit is a tree. (III) No tree is a branch.