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

(1) Symphonies are more edifying than plays but less edifying than organ concerts.  This could be rewritten:

Organ concerts > symphonies > plays

(2) Silence is more edifying than organ concerts: silence > organ concerts

Thus, we can combine these to get:

Silence > organ concerts > symphonies > plays

Therefore, it is true to say that plays are less edifying than silence.

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

(1) Dragons are more dangerous than roaches but fleas are more dangerous than dragons. This can be rewritten:

Fleas > dragons > roaches

(2) Fleas are less dangerous than bees: fleas < bees

This can be rewritten: bees > fleas

Thus we can combine these to say: bees > fleas > dragons > roaches

Thus, by the strange logic that we have been given, it is true to say bees are more dangerous than roaches (and dragons even!).

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

(1) Paschal is more cunning than Jordan but less cunning than Douglas. This can be rewritten:

Douglas > Paschal > Jordan

(2) Douglas is less cunning than Mark but more cunning than Peter. This can be rewritten:

Mark > Douglas > Peter

Now, let's pay attention to the pertinent information. All that we know about Peter is that he is less cunning than Douglas. This means that he could be more cunning than Paschal, less cunning than Paschal and more cunning than Jordan, or less cunning than Jordan.

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.