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.

Let’s use symbols from math to help us understand this. "Greater than" (>) will mean "has more fun," and "less than" (<) will mean "has less fun."

(1) Teddy has more fun than Jack: Teddy > Jack

(2) Franklin has less fun than Jack: Franklin < Jack

This could also be written: Jack > Franklin

Therefore, we could string all of these together into:

Teddy > Jack > Franklin

Therefore, (3) Teddy > Franklin does hold.

Note that when something is "tedious" it is boring, hence, less exciting than something else. Let’s use symbols from math to help us understand this problem. “Greater than” (>) will mean “more exciting,” and “less than” (<) will mean “more tedious (i.e. less exciting).”

(1) John is more tedious than Robert: John < Robert

Notice that this could be rewritten: Robert > John

(2) Robert is more exciting than Alan: Robert > Allen

Therefore, our information only tells us that Robert is more exciting than both John and Allen. It says nothing about the relationship between Allen and John.

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 “taller,” and “less than” (<) will mean “shorter.”

(1) Andrew is taller than Abraham: Andrew > Abraham

(2) Abraham is shorter than Charles: Abraham < Charles

This could be rewritten: Charles > Abraham

Another way of looking at these two would be:

(1) Abraham < Andrew

(2) Abraham < Charles

This tells us that Abraham is shorter than Andrew and Charles. It tells us nothing about the relationship between Charles and Andrew.

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.

Since we only know that the first two sentences are true, the truthfulness of the third sentence is uncertain. The first two sentences compare the popularity of peanut butter and jelly sandwiches with tuna sandwiches. Roast beef is never mentioned in the first two sentences, so we can not determine if it is the most popular or not.

The only two facts that we know for certain are:

1. Sarah gets better grades in math than Luis; and

2. Luis gets better grades in science than Sarah.

These are both quantifiable statements. This means that we can put an absolute number to each statement. Although we don't know what the actual grades are, we know that Sarah's grades are better in math and Luis' grades are better in science.

The third sentence, "Luis is a better student than Sarah" has many unknown variables. We don't know what grades either student receives in any other class. We don't know how much better Sarah is in math than Luis, or how much better Luis is in science than Sarah. Finally, the phrase "better student" is not defined. This could mean higher grades in classes, or it could mean higher grades on standardized tests. "Better student" could even mean the student that studies the hardest or pays the best attention in class. For these reasons, the truthfulness of the third sentence is 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.

Based on the information from the first two sentences, the third sentence must be false. Sentence 1 states that Magali will take her vacation "as soon as" she has earned the money. This implies that Magali will not wait, but will go on vacation immediately. Sentence 2 states that Magali is working an extra job to earn the money more quickly. This sentence also implies that Magali has not earned enough money yet. Consequently, the third sentence stating that Magali has earned enough money to go on vacation must be false.