Let's use symbols from math to help us understand this:

(1) Jeremy is taller than Jean: Jeremy > Jean

(2) John is shorter than Jeremy: John < Jeremy

This could be rewritten: Jeremy > John

Thus, we know that Jeremy is taller than Jean and John; however, we do not know anything about the relationship between John and Jean.

Let’s use symbols from math to help us understand this.

(1) Thomas is smarter than Luca: Thomas > Luca

(2) Luca is smarter than John: Luca > John

We could string these together as well:

Thomas > Luca > John

John is not smarter than Thomas; therefore, this is false.

Let’s use symbols from math to help us understand this.

(1) Baruch is weirder than Frederick: Baruch > Frederick

(2) Frederick is weirder than Arthur: Frederick > Arthur

These can all be combined to give us: 

Baruch > Frederick > Arthur

It is indeed the case that (3) Baruch > Arthur.

Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "more known," and "less than" (<) will mean "more unknown."

(1) Godfrey is more unknown than Henry: Godfrey < Henry

This could be rewritten: Henry > Godfrey

(2) Henry is better known than Giles: Henry > Giles

Thus, we know that Henry is more known than both Giles and Godfrey; however, this does not tell us anything about the relationship between Giles and Godfrey.  Therefore (3) is uncertain.

Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "has more fun," and "less than" (<) will mean "has less fun."

(1) Teddy has more fun than Jack: Teddy > Jack

(2) Franklin has less fun than Jack: Franklin < Jack

This could also be written: Jack > Franklin

Therefore, we could string all of these together into:

Teddy > Jack > Franklin

Therefore, (3) Teddy > Franklin does hold.

Let’s use symbols from math to help us understand this.  “Greater than” (>) will mean “more difficult,” and “less than” (<) will mean “easier.”

(1) Physics is more difficult than chemistry: Physics > chemistry

This could be rewritten: Chemistry < physics

(2) Chemistry is easier than philosophy: Chemistry < philosophy

Therefore, this tells us that chemistry is easier than the other two subjects.  However, it does not tell us anything about the relationship between philosophy and physics.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “harder to drive in,” and “less than” (<) will mean “easier to drive in.”

(1) It is easier to drive in snow than it is in ice: snow < ice

(2) It is harder to drive in snow than in rain: snow > rain

This could be rewritten: rain < snow.

All of these could be combined to give us: rain < snow < ice.

This means that rain is indead easier to drive in that ice.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more efficient than,” and “less than” (<) will mean “less efficient than.”

(1) Nuclear power is more efficient than coal power: nuclear > coal

This could be rewritten as: coal < nuclear

(2) Coal power is less efficient than gas power: coal < gas

Thus, we are told that coal is less efficient than both nuclear and gas; however, we are told nothing about the relationship between nuclear and gas power.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more on the road,” and “less than” (<) will mean “less on the road.”

(1) There are more cabs than trucks on the roads in New York City: cabs > trucks

This could be rewritten as: trucks < cabs

(2) There are more motorcycles than there are trucks on the roads in New York City: motorcycles > trucks

This could be rewritten as: trucks < motocycles

Thus, we are actually only being told something about trucks—there are fewer of them than both cabs and motorcycles (in New York City).  Thus, we cannot say anything about the relationship between the number of cabs and the number of motorcycles.

Let’s use symbols from math to help us understand this.  “Greater than” (>) will mean “has a greater salary than,” and “less than” (<) will mean “has a lower salary than.”

(1) George has a greater salary than John: George > John

(2) Filbert has a lower salary than George: Filbert < George

This could be rewritten as: George > Filbert

This means that we are being told that George has a greater salary than both John and Filbert; however, it tells us nothing about the relation between these latter two men.