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.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is smarter than.”

(1) Paul is smarter than Peter: Paul > Peter

(2) Peter is smarter than Andrew: Peter > Andrew

These could be combined to give us:

Paul > Peter > Andrew

Therefore, it is false to say that Andrew is smarter than Paul.

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

(1) Emmanuel is more boring than David: Emmanuel > David

(2) Emmanuel is less boring than John: Emmanuel < John

This could be rewritten: John > Emmanuel

We could thus combine these as: John > Emmanuel > David

Thus it is false to say that David is more boring than John.

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

(1) Children are more immature than adults: children < adults

This could be rewritten: adults > children

(2) Adults are more mature than teenagers: adults > teenagers

Therefore, all that we are being told is that adults are more mature than both teenagers and children. Nothing can be inferred regarding the relative status of teenagers and children.

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

(1) Thomas is braver than Henry: Thomas > Henry

(2) Thomas is more cowardly than Athanasius: Thomas < Athanasius

Note, this could be rewritten: Athansius > Thomas

Thus, we could put together the two statements and get:

Athanasius > Thomas > Henry

Therefore, it is true to say that Athanasius is braver than Henry.