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

(1) Rachel is busier than Brandon but less busy than Matthew. This can be rewritten:

Matthew > Rachel > Brandon

(2) Matthew is less busy than Thomas but busier than Nicholas. This can be rewritten:

Thomas > Matthew > Nicholas

Now, since know that Thomas is busier than Matthew, who is busier than Rachel, we can combine our statements into:

Thomas > Matthew > Rachel > Brandon

This means that we can indeed say that Thomas is busier than Brandon.

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

(1) Margaret is kinder than Douglas: Margaret > Douglas

(2) Douglas is nastier than Patrick: Douglas < Patrick

This can be rewritten: Patrick > Douglas

Note that these merely tell us that Douglas is nastier than both Margaret and Patrick. It tells us nothing about the relationship between these latter two.

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

(1) Valerie is kinder than Carol: Valerie > Carol

(2) Patricial is much nastier than Carol: Patricia < Carol

This can be rewritten: Carol > Patricia

Thus, we can combine all of these into:

Valerie > Carol > Patricia

Therefore, it is not true to say that Patricia is kinder than Valerie.

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

(1) Palestrina’s music is more beautiful than that of Tallis: Palestrina > Tallis

(2) Gregorian chant is more beautiful than Palestrina’s music: Gregorian chant > Palestrina

Thus, we can combine them to get:

Gregorian chant > Palestrina > Tallis

This is the same thing as saying that Tallis' music is less beautiful than Gregorian chant.

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

(1) Tallis’ music is more enjoyable than Byrd’s: Tallis > Byrd

(2) Haydn’s music is less enjoyable than Byrd’s: Haydn < Byrd

This could be rewritten: Byrd > Haydn

Thus, combining everything, we would have:

Tallis > Byrd > Haydn

It is false to say that Tallis' music is less enjoyable than Haydn's.

When someone is aggressive, he or she is confrontational or forceful. Such a person is the opposite of a passive person, that is, someone who less likely to be active in responding or undertaking a task. Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “more aggressive,” and “less than” (<) will mean “more passive (i.e. less aggressive).”

(1) Daniel is more passive than Albert: Daniel < Albert

This can be rewritten: Albert > Daniel

(2) Isidore is more aggressive than Albert: Isidore > Albert

We can combine these to get:

Isidore > Albert > Daniel

Thus, it is true to say that Isidore is more aggressive than Daniel.

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

(1) Cholesterol is healthier than saturated fat: cholesterol > saturated fat

(2) Saturated fat is healthier than cyanide but less healthy than unsaturated fat.

We get two statements from this:

(a) saturated fat > cyanide

(b) saturated fat < unsaturated fat

These can be combined to give us:

unsaturated fat > saturated fat > cyanide

Now, all we know is that cholesterol is more healthy than saturated fat. We do not know its relationship to unsaturated fat. It could be more or less healthy; therefore, the conclusion is uncertain.

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

(1) Theobald finished the race before Leonard and Ronald.

We get two statements from this: 

(a) Theobald < Leonard

(b) Theobald < Ronald

(2) Patrick finished the race after Theobald and before Leonard.

We get two statements from this: 

(a) Patrick > Theobald

(b) Patrick < Leonard

This can be rewritten: Leonard > Patrick

These can be combined to give us:

Leonard > Patrick > Theobald

Now, we know that Ronald is somewhere after Theobald (thus to the left of the > before Theobald); however, we cannot say anything about his relationship between Ronald and Patrick; therefore, the conclusion is uncertain.

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

(1) Monophony is plainer than homophony and polyphony

We get two statements from this:

(a) monophony < homophony

(b) monophony < polyphony

(2) Heterophony is more complex than monophony: heterophony > monophony

Notice, this is the same thing as saying: monophony < heterophony

Thus, all we have are a set of statements that tell us that monophony is plainer than all of the others. This tells us nothing about the relationship between polyphony and heterophony.

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

(1) Regulations are more annoying than taxes and fines.

We get two statements from this: 

(a) regulations > taxes

(b) regulations > fines

(2) Fines are less annoying than arbitrations: fines < arbitrations

This can be rewritten as arbitrations > fines

Notice that these statments tell us that arbitrations and regulations are both more annoying than fines.  However, they do not tell us the relationship between the two.