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

(1) Fantasy is more popular than biographies but less popular than self-help. This gives us:

self-help > fantasy > biographies

(2) Self-help is less popular than Thomism: self-help < Thomism

This is the same thing as: Thomism > self-help

That means that we can say:

Thomism > self-help > fantasy > biographies

Therefore, it is true to say that Thomism is more popular than biographies.

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

(1) Nominalism is more problematic than conceptualism but less problematic than direct realism. This gives us:

direct realism > nominalism > conceptualism

(2) Conceptualism is more problematic than Poinsotiannism: conceptualism > Poinsotiannism

We can combine (1) and (2) to get:

direct realism > nominalism > conceptualism > Poinsotiannism

This means that it is false to say that Poinsotiannism is more problematic than direct realism. The complete oposite is the truth based on these premises.

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

(1) Mathematics is more abstract than natural philosophy but less abstract than metaphysics. This gives us:

Metaphysics > mathematics > natural philosophy

(2) Optics is more abstract than natural philosophy but less abstract than mathematics. This gives us:

Mathematics > optics > natural philosophy

This tells us that we can say:

Metaphysics > mathematics > optics > natural philosophy

It is not true to say that optics is more abstract than metaphysics.

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) Hamburgers are more enjoyable than yogurt but less enjoyable than tuna steak. This gives us:

Tuna steak > hamburgers > yogurt

(2) Tuna steak is more enjoyable than bacon: tuna stead > bacon

This does not, however, tell us anything about the relative positions of bacon and hamburgers; therefore the conclusion is uncertain.

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

(1) Cigars have oilier smoke than cigarettes but less oily smoke than pipes. This can be written:

Pipes > cigars > cigarettes

(2) Cornhusks have oilier smoke than cigars: cornhusks > cigar

Therefore, we can combine these to get:

Cornhusks > pipes > cigars > cigarettes

This means that cigarettes do indeed have less oily smoke than cornhusks.

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 than.”

(1) Milk is healthier than apple juice and less healthy than carrot juice. This can be rewritten:

Carrot juice > milk > apple juice

(2) Apple juice is healthier than syrup water: apple juice > syrup water

We can combine all of these to get:

Carrot juice > milk > apple juice > syrup water

It is thus true to say that syrup water is less healthy than milk.

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

(1) Cajetan is more logical than Sylvester: Cajetan > Sylvester

(2) John is less logical than Cajetan but more logical than Francisco.  This can be rewritten:

Cajetan > John > Francisco

Notice that all we need to pay attention to is the second statement.  Here, it states that Fracisco is indeed less logical than Cajetan.

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.