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

(1) Computers are more complex than typewriters, which are more complex than pencils: computers > typewriters > pencils

(2) Pencils are less complex than ink wells but more complex flint stones: ink wells > pencils > flint stones

Now, since typewriters > pencils and pencils > flint stones, we can say that typewriters > flint stones; therefore, the statement, "Typewriters are more complex than flint stones," is true.

Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is better at.”

(1) For Lauren: cooking > sewing

(2) For Barbara: scheduling > (Lauren sewing)

Now, let's translate (3): (Barbara scheduling) > (Lauren cooking)

Okay, now we know that Barbara is better at scheduling than Lauren was at sewing. Likewise, we know that Lauren is better at cooking than she is at sewing. Thus, Barbara's scheduling and Lauren's cooking are both better than Lauren's sewing; however, we do not know the relationship between Barbara's scheduling and Lauren's cooking; therefore, the conclusion is uncertain.

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

(1) For Nancy: vegetables > fruits

(2) For Tim: beers > (Nancy fruits)

This means that Tim's pickiness about beers is either greater than Nancy's pickiness about vegetables or is less than that but still greater than her pickiness about fruits. Thus, we cannot conclude one way or the other regarding the relationship between Nancy's pickiness regarding vegetables and Tim's pickiness concerning beers (based on our information).

Now, to be conceited is to be overly proud. Thus, humility is the opposite of such conceit. Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is more conceited than (is less humble),” and “less than” (<) will mean “is less conceited than.”

(1) John is less conceited than Jeremy but more conceited than George: George < John < Jeremy

(2) George is less humble (i.e. more conceited) than William: George > William. This could also be rewritten: William < George

Thus, we can combine 1 and 2 to get: William < George < John < Jeremy

It is false to say that that John is Less conceited than William.

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

(1) Nicholas is wealthier than Scott but poorer than Leslie: Leslie > Nicholas > Scott

(2) Leslie is poorer than Pamela and wealthier than Barbara: Pamela > Leslie > Barbara

Now, we know that Pamela is wealthier than Leslie, so we can write:

Pamela > Leslie > Nicholas > Scott

This tells us that Pamela is wealthier than Scott.

When someone is "industrious," he or she is hard working—not lazy. Let’s use symbols from math to help us understand this. “Greater than” (>) will mean “is lazier than,” and “less than” (<) will mean “is less lazy (more industrious) than.”

(1) Richard is lazier than Brandon who is more industrious than Larry. This gives us two statements:

(a) Richard > Brandon

(b) Brandon < Larry, which could also be rewritten: Larry > Brandon

(2) Larry is lazier than Paul but more industrious than Todd. This gives us two statements as well:

(a) Larry > Paul

(b) Larry < Todd, which could also be rewritten: Todd > Larry

Now, we could thus take 1.b and 2.b to get:

Todd > Larry > Brandon

Thus, it is true that Todd is lazier than Brandon

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

(1) Jonathan is more intelligent than Jeremy, who is more intelligent than Lola: Jonathan > Jeremy > Lola

(2) Regina is less intelligent than Lola, who is more intelligent than Lena.  This gives us:

(a) Regina < Lola, which could be rewritten: Lola > Regina

(b) Lola > Lena

Now, Jonathan is more intelligent than Lola, who is more intelligent than both Regina and Lena; therefore, Jonathan is more intelligent than Regina and Lena.

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).