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

(1) Karen is more depressed than Carol, who is less depressed than Edward. This gives us two statements:

(a) Karen > Carol

(b) Carol < Edward, which is the same as: Edward > Carol

(2) Edward is more depressed than Paula, who is more depressed than Byron: Edward > Paula > Byron

Now, we know that Byron is less depressed than Edward and that Carol likewise is less depressed than Edward; however, we cannot say anything about the relative depression of Carol and Byron. Thus, the third statement is merely uncertain.

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) Sarah is busier than Leo, who is busier than Harold: Sarah > Leo > Harold

(2) Harold is less busy than both Peter and Paul. This gives us two statements:

Harold < Peter, which could be written: Peter > Harold

Harold < Paul, which could be written: Paul > Harold

Now, we know that Sarah is busier than Harold, as is the cause with Paul; however, Paul could be much, much, much busier than Harold and hence be busier than Sarah is. Also, Paul could be only slightly more busy than Harold but still less busy than Leo, hence being less busy than Sarah. Thus, the third statement provides us with a merely uncertain conclusion.

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

(1) Sally is more successful than Luke but less successful than Peter: Peter > Sally > Luke

(2) Luke is less successful than Ronald, who is less successful than Mildred: Luke < Ronald < Mildred

For perspective, let us rewrite this as : Mildred > Ronald > Luke

Now, what these two tell us is that Luke is the least successful of all the people listed; however, notice that there is no sort of overlap between the two otherwise; therefore, we cannot say anything about the relative positions of Peter and Mildred (except that they are both more successful than Luke).

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

(1) Ulric is more violent than Aethelwold: Ulric > Aethelwold

(2) Beowulf is more violent than Aethelwold but less violent than Aelfric: Aelfric > Beowulf > Aethelwold

These both tell us that Aethelwold is the least violent; however, it does not tell us the exact relationship between Ulric and Aelfric. We could conclude either way regarding their relative violence.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is hotter than (or warmer than),” and “less than” (<) will mean “is cooler than (is less hot than).”

(1) The Sahara is hotter than the Alps: Sahara > Alps

(2) My teakettle is warmer than the Alps but cooler than my oven: oven > teakettle > Alps

Both of these tell us that the Alps are cooler than the Sahara and my oven; however, they do not tell us anything about the relative positions of my oven and the Sahara; therefore, we must mark this as being uncertain.

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) Oatmeal is healthier than chili but less healthy than oysters: oysters > oatmeal > chili

(2) Oysters are less healthy than ham: oysters < ham

This could be rewritten: ham > oysters

By combining our statements, this likewise lets us write: 

ham > oysters > oatmeal > chili

Therefore, according to the logic of these statements, it is true to say that ham is healthier than chili.

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

(1) Frederick is louder than Bonaventure but softer than Aaron: Aaron > Frederick > Bonaventure

(2) Aaron is louder than Helga who is louder than Bonaventure: Aaron > Helga > Bonaventure

Now, these two statements do tell us that Frederick and Helga both are softer than Aaron and louder than Bonaventure.  However, they do not provide enough information to say which is louder than the other.

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

(1) Geoffrey is less famous than William but more famous than Reuel: William > Geoffrey > Reuel

(2) Reuel is more famous than Clives: Reuel > Clives

We can combine these two statements to get:

William > Geoffrey > Reuel > Clives

Therefore, it is indeed true to say that Geoffrey is more famous than Clives.

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

(1) It is simpler to fabricate bricks than it is to fabricate cut stone: bricks < cut stones

Notice that we can rewrite this as: cut stones > bricks

(2) Cut stone is more difficult to fabricate than mud roofs but less complicated to fabricate than plutonium rods: plutonium rods > cut stone > mud roofs

Now, we combine the second form of (1) with (2) and get:

plutonium rods > cut stone > bricks

Therefore, it is false to say that plutonium rods are simpler to fabricate than bricks.

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

(1) Porphyry is less mystifying than Plotinus, who is more mystifying than Ibn Gabirol. This gives us two statements, really:

(a) Porphyry < Plotinus, which could also be read: Plotinus > Porphyry

(b) Plotinus > Ibn Gabirol

(2) Avicenna is less mystifying than Ibn Gabirol: Avicenna < Ibn Gabirol

This could be rewritten: Ibn Gabirol > Avicenna

Now, this problem is meant to overwhelm you with data. Only pay attention to the relevant facts. We only need information from (1). Porphyry is less mystifying than Plotinus (see 1.a). The same holds for Ibn Gabirol (see 1.b). This does not, however, tell us anything about their relation to each other.