## logical problems

#### Discussion Question

Each problem consists of three statements. Based on the first two statements, the third statement may be true, false, or uncertain.

###### Tanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: B - false

Because the first two statements are true, Eric is the youngest of the three, so the third statement must be false.

###### Blueberries cost more than strawberries. Blueberries cost less than raspberries. Raspberries cost more than strawberries and blueberries. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: A - true

Because the first two statements are true, raspberries are the most expensive of the three.

###### All the trees in the park are flowering trees. Some of the trees in the park are dogwoods. All dogwoods in the park are flowering trees. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: A - true

All of the trees in the park are flowering trees, So all dogwoods in the park are flowering trees.

###### Mara runs faster than Gail. Lily runs faster than Mara. Gail runs faster than Lily. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: B - false

We know from the first two statements that Lily runs fastest. Therefore, the third statement must be false.

###### Apartments in the Riverdale Manor cost less than apartments in The Gaslight Commons. Apartments in the Livingston Gate cost more than apartments in the The Gaslight Commons. Of the three apartment buildings, the Livingston Gate costs the most. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: A - true

Since the Gaslight Commons costs more than the Riverdale Manor and the Livingston Gate costs more than the Gaslight Commons, it is true that the Livingston Gate costs the most.

###### The Kingston Mall has more stores than the Galleria. The Four Corners Mall has fewer stores than the Galleria. The Kingston Mall has more stores than the Four Corners Mall. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: A - true

From the first two statements, you know that the Kingston Mall has the most stores, so the Kingston Mall would have more stores than the Four Corners Mall.

###### All the tulips in Zoe's garden are white. All the pansies in Zoe's garden are yellow. All the flowers in Zoe's garden are either white or yellow If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: C - uncertain

The first two statements give information about Zoe's tulips and pansies. Information about any other kinds of flowers cannot be determined.

###### During the past year, Josh saw more movies than Stephen. Stephen saw fewer movies than Darren. Darren saw more movies than Josh. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: C - uncertain

Because the first two sentences are true, both Josh and Darren saw more movies than Stephen. However, it is uncertain as to whether Darren saw more movies than Josh.

###### Rover weighs less than Fido. Rover weighs more than Boomer. Of the three dogs, Boomer weighs the least. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: A - true

According to the first two statements, Fido weighs the most and Boomer weighs the least.

###### All the offices on the 9th floor have wall-to-wall carpeting. No wall-to-wall carpeting is pink. None of the offices on the 9th floor has pink wall-to-wall carpeting. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: A - true

If no wall-to-wall carpeting is pink and all the offices have wall-to-wall carpeting, none of the offices has pink wall-to-wall carpeting.

###### Class A has a higher enrollment than Class B. Class C has a lower enrollment than Class B. Class A has a lower enrollment than Class C. If the first two statements are true, the third statement is
 A true B false C uncertain
 ANS: B - false

From the first two statements, we know that of the three classes, Class A has the highest enrollment, so the third statement must be false.