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.

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

(1) The tuba has a more beautiful tone than the trumpet: tuba > trumpet

(2) The flute has a less beautiful tone than the trumpet: flute < trumpet

This could be rewritten: trumpet > flute

Therefore, we could combine these to get:

tuba > trumpet > flute

Therefore, it is not true to say that the tuba has a less beautiful tone than the flute.

Let’s use symbols from math to help us understand this and treat "wakes" as the opposite of "makes drowsier (i.e. less awake)." “Greater than” (>) will mean “wakes,” and “less than” (<) will mean “makes drowsier.”

(1) Oatmeal wakes Sara better than chocolate does: oatmeal > chocolate

(2) Peanut butter makes Sara drowsier than does chocolate: peanut butter < chocolate

This could be rewritten: chocolate > peanut butter

Note that we could combine all of these into:

oatmeal > chocolate > peanut butter

Thus, oatmeal does indeed wake Sara better than peanut butter.

Some vocabulary is necessary first. "Beneficient" means "giving or generous." (Think of "benefit," which is related to this word). To be "miserly" is to be "stingy," not wishing to give out money or gifts.

Now, let's use symbols from math to help us understand this.  “Greater than” (>) will mean “more beneficent,” and “less than” (<) will mean “more miserly (i.e. less beneficent).”

(1) Scott is more beneficent than Michael: Scott > Michael

Note that this could be rewritten: Michael < Scott

(2) Michael is more miserly than Peter: Michael < Peter

Therefore, all that we are being told is that Michael is less beneficent than both of the other men. There is no necessary relationship described about Scott and Peter.

Note that when something is "tedious" it is boring, hence, less exciting than something else. Let’s use symbols from math to help us understand this problem. “Greater than” (>) will mean “more exciting,” and “less than” (<) will mean “more tedious (i.e. less exciting).”

(1) John is more tedious than Robert: John < Robert

Notice that this could be rewritten: Robert > John

(2) Robert is more exciting than Alan: Robert > Allen

Therefore, our information only tells us that Robert is more exciting than both John and Allen. It says nothing about the relationship between Allen and John.

When something is trivial, it is unimportant. Therefore, let's use symbols from math to help us understand this. “Greater than” (>) will mean “more important,” and “less than” (<) will mean “less important (i.e. trivial).”

(1) Ibn Sina is more important than Ibn Rushd: Ibn Sina > Ibn Rushd

Notice that this could be rewritten: Ibn Rushd < Ibn Sina

(2) Ibn Rushed is more trivial than Alfarabi: Ibn Rushd < Alfarabi

Therefore, our data is telling us that Ibn Rushd is more trivial (or less important) than Alfarabi and Ibn Sina.  However, it does not provide us with any information regarding the relationship between Alfarabi and Ibn Sina.

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

(1) Frank is poorer than Joseph: Frank < Joseph

Notice that this could be rewritten: Joseph > Frank

(2) Pio is wealthier than Joseph: Pio > Joseph

Notice that we can combine all of these to get:

Pio > Joseph > Frank

Therefore, it is true that Frank is poorer than Pio.