Logical Problems Questions

Spatial reasoning – cardinal directions among three towns Given: Middletown is north of Centerville. Centerville is east of Penfield. Question: If those two facts are true, is the statement “Penfield is northwest of Middletown” true, false, or uncertain?

Categorical logic – hair length and tail length for “Gangles” Given: All spotted Gangles have long tails. Short-haired Gangles always have short tails. Question: If those two facts are true, is the statement “Long-tailed Gangles never have short hair” true, false, or uncertain?

Categorical logic – color and features of “Signots” and “Lamels” Given: All Lamels are Signots with buttons. No yellow Signots have buttons. Question: If those two facts are true, is the statement “No Lamels are yellow” true, false, or uncertain?

Logical reasoning — Evaluate the third statement based only on the first two premises Premise 1: The hotel is two blocks east of the drugstore. Premise 2: The market is one block west of the hotel. Claim (to evaluate): The drugstore is west of the market. Choose whether the claim is true, false, or uncertain from the premises given.

Logical reasoning — Determine if the conclusion follows from the premises Premise 1: A toothpick is useful. Premise 2: Useful things are valuable. Claim (to evaluate): A toothpick is valuable.

Logical reasoning — Order-of-dressing puzzle: does the final claim follow? Premise 1: Tom puts on his socks before he puts on his shoes. Premise 2: He puts on his shirt before he puts on his jacket. Claim (to evaluate): Tom puts on his shoes before he puts on his shirt.

Quantitative logic — Compare item costs from linked equivalences Premise 1: Three pencils cost the same as two erasers. Premise 2: Four erasers cost the same as one ruler. Claim (to evaluate): Pencils are more expensive than rulers.

Transitive speed comparison — Decide if the final relation is implied Premise 1: Taking the train across town is quicker than taking the bus. Premise 2: Taking the bus across town is slower than driving a car. Claim (to evaluate): Taking the train across town is quicker than driving a car.

Windiness ordering — Determine if the final comparison is entailed Premise 1: Cloudy days tend to be more windy than sunny days. Premise 2: Foggy days tend to be less windy than cloudy days. Claim (to evaluate): Sunny days tend to be less windy than foggy days.

Parking-order reasoning — Does the final placement necessarily follow? Premise 1: A sedan is parked to the right of a pickup and to the left of a sport utility vehicle (SUV). Premise 2: A minivan is parked to the left of the pickup. Claim (to evaluate): The minivan is parked between the pickup and the sedan.

Comparative quality — Does the third statement follow from the first two? Premise 1: The bookstore has a better selection of postcards than the newsstand. Premise 2: The selection of postcards at the drugstore is better than at the bookstore. Claim (to evaluate): The drugstore has a better selection of postcards than the bookstore or the newsstand.

Quantitative comparison of counts — Are the color totals consistent with the claim? Premise 1: A jar of jelly beans contains more red beans than green. Premise 2: There are more yellow beans than red. Claim (to evaluate): The jar contains fewer yellow jelly beans than green ones.

Set logic with dogs — Identify which statement must be true from the given facts Fact 1: All dogs like to run. Fact 2: Some dogs like to swim. Fact 3: Some dogs look like their masters. Which of the following must also be a fact? I: All dogs who like to swim look like their masters. II: Dogs who like to swim also like to run. III: Dogs who like to run do not look like their masters.

Logical reasoning — Deductive facts (choose the statement that must be true) Facts: Jessica has four children. Two children have blue eyes and two have brown eyes. Half of the children are girls. Which of the following statements must also be a fact? I: At least one girl has blue eyes. II: Two of the children are boys. III: The boys have brown eyes.

Logical reasoning — Set relations (choose the statement that must be true) Facts: All drink mixes are beverages. All beverages are drinkable. Some beverages are red. Which statements must also be facts? I: Some drink mixes are red. II: All beverages are drink mixes. III: All red drink mixes are drinkable.

Logical reasoning — Birds and chickens (choose the statement that must be true) Facts: All chickens are birds. Some chickens are hens. Female birds lay eggs. Which statements must also be facts? I: All birds lay eggs. II: Some hens are birds. III: Some chickens are not hens.

Logical reasoning — Hats, colors, and caps (choose the statement that must be true) Facts: All hats have brims. There are black hats and there are blue hats. Baseball caps are hats. Which statements must also be facts? I: All caps have brims. II: Some baseball caps are blue. III: Baseball caps have no brims.

Logical reasoning — Costs and materials (choose the statement that must be true) Facts: Eyeglass frames cost between $35 and $350. Some eyeglass frames are made of titanium. Some eyeglass frames are made of plastic. Which statements must also be facts? I: Titanium frames cost more than plastic frames. II: Expensive frames last longer than cheap frames. III: Only a few frames cost less than $35.

Logical reasoning — “Most” versus “All” (choose the statement that must be true) Facts: Most stuffed toys are stuffed with beans. There are stuffed bears and there are stuffed tigers. Some chairs are stuffed with beans. Which statements must also be facts? I: Only children's chairs are stuffed with beans. II: All stuffed tigers are stuffed with beans. III: Stuffed monkeys are not stuffed with beans.

Logical reasoning — Truth tellers and sometimes-liars (choose the statement that must be true) Facts: Mary said, 'Ann and I both have cats.' Ann said, 'I don't have a cat.' Mary always tells the truth, but Ann sometimes lies. Which statements must also be facts? I: Ann has a cat. II: Mary has a cat. III: Ann is lying.