Question 1

If A is sufficient for B, then B is necessary for

Accepted Answer

If A is sufficient for B, it means that the presence of A guarantees the presence of B. Therefore, if B is not present, then A must not be present either. This means that B is necessary for A.

Question 2

Being at least eighteen is a necessary condition for voting in the United States.

Accepted Answer

In the United States, individuals must be at least 18 years old to vote in federal, state, and local elections, making being 18 a necessary condition for voting.

Question 3

Being a rectangle with four equal sides is necessary and sufficient for being a square.

Accepted Answer

A square is a special type of rectangle that has all four sides of equal length, so having four equal sides (and right angles, as implied by being a rectangle) is both necessary (required for it to be a square) and sufficient (enough on its own to define it as a square).

Question 4

The presence of oxygen is a sufficient condition for a candle to be burning.

Accepted Answer

The presence of oxygen is a necessary condition for a candle to burn, but it is not sufficient on its own; a candle also needs a fuel source (like wax) and heat to ignite.

Question 5

A candle burning is a sufficient condition for the presence of oxygen.

Accepted Answer

A candle burning requires oxygen to sustain the combustion process, so if a candle is burning, it indicates that oxygen is present.

Question 6

If one state affairs, A, is a necessary condition for another state of affairs, B, then
A) A cannot occur without B occurring.
B) B cannot occur without A occurring.
C) Both a and
D) Neither a nor

Accepted Answer

B cannot occur without A occurring. This is because a necessary condition means that for B to happen, A must first occur. However, A can occur without leading to B.

Question 7

If A is a sufficient condition for B, then B is
A) A necessary condition for
B) A sufficient condition for
C) Both necessary and sufficient for
D) Neither necessary nor sufficient for

Accepted Answer

If A is a sufficient condition for B, it means that whenever A occurs, B must also occur. However, B can occur without A, making B a necessary condition for A but not a sufficient one.

Question 8

For a human to live, being able to breathe is
A) A necessary condition.
B) A sufficient condition.
C) Both a necessary and a sufficient condition.
D) Neither a necessary nor a sufficient condition.

Accepted Answer

Being able to breathe is a necessary condition for a human to live because without oxygen, vital bodily functions cannot be sustained. However, it is not a sufficient condition on its own, as other factors like food, water, and protection from fatal injuries or conditions are also required for life.

Question 9

For a rectangle to be considered a square, having four sides of equal length is
A) A necessary condition.
B) A sufficient condition.
C) Both a necessary and a sufficient condition.
D) Neither a necessary nor a sufficient condition.

Accepted Answer

For a rectangle to be considered a square, it must have four sides of equal length. This condition is both necessary (a square cannot exist without it) and sufficient (if a rectangle has four sides of equal length, it is a square).

Question 10

To be a college student, owning a computer is
A) A necessary condition.
B) A sufficient condition.
C) Both a necessary and a sufficient condition.
D) Neither a necessary nor a sufficient condition.

Accepted Answer

Owning a computer is not a necessary condition to be a college student because one can be a student without owning a computer, as they might access computers through other means (libraries, computer labs, etc.). It is also not a sufficient condition because simply owning a computer does not automatically make one a college student; there are other requirements (admissions, enrollment, etc.).

Question 11

For a shape to be a triangle, having three sides is
A) A necessary condition.
B) A sufficient condition.
C) Both a necessary and a sufficient condition.
D) Neither a necessary nor a sufficient condition.

Accepted Answer

The answer of For a shape to be a triangle,...

Question 12

For winning a race, crossing the finish line first is
A) A necessary condition.
B) A sufficient condition.
C) Both a necessary and a sufficient condition.
D) Neither a necessary nor a sufficient condition.

Accepted Answer

Crossing the finish line first is both a necessary and a sufficient condition for winning a race. It is necessary because without doing so, one cannot win the race; it is sufficient because doing so guarantees a win, assuming all rules are followed.

Question 13

"You can't be a good athlete without studying ballet." Which of these would be the best way to prove that this statement is false?
A) Show an example of a good athlete who has studied ballet.
B) Show an example of a good athlete who has NOT studied ballet.
C) Show an example of a ballet student who is a good athlete.
D) Show an example of a ballet student who is NOT a good athlete.

Accepted Answer

To disprove the statement that one cannot be a good athlete without studying ballet, it is most effective to provide an example of a good athlete who has never studied ballet. This directly contradicts the claim by showing that studying ballet is not a prerequisite for athletic success.

Question 14

Claim: "Caring about students is a necessary condition for being a good teacher." Objection: "Lots of people care about students and still aren't good teachers." Does this objection show that the claim is wrong?
A) No, because the claim is only that caring is necessary, not sufficient.
B) No, because caring can be necessary and still be sufficient.
C) Yes, because caring about students is both necessary and sufficient.
D) Yes, because it's true that caring is not sufficient to make one a good teacher.

Accepted Answer

The objection does not disprove the claim because it misunderstands the claim's scope. The claim suggests that caring is a necessary condition, not that it alone makes someone a good teacher. The objection points out that caring alone is not enough, which does not contradict the claim that caring is necessary, just not sufficient on its own.

Question 15

A certain college requires all students to have physical education credits to graduate. For this college, physical education is
A) A necessary condition for graduating.
B) A sufficient condition for graduating.
C) Both necessary and sufficient for graduating.
D) Neither necessary nor sufficient for graduating.

Accepted Answer

Physical education credits are a necessary condition for graduating because students must have them to graduate, but having them alone is not enough to ensure graduation; students must also meet other requirements.

Question 16

A college offers an elective course in the history of philosophy. Students may choose to take it to fill a humanities requirement or they make take a different course. For this college, the history of philosophy course is
A) A necessary condition for graduating.
B) A sufficient condition for graduating.
C) Both necessary and sufficient for graduating.
D) Neither necessary nor sufficient for graduating.

Accepted Answer

Since students can choose to take the history of philosophy course or a different course to fulfill a humanities requirement, it is not necessary for graduating. Additionally, taking this course alone is not enough to graduate, as students must meet other requirements as well, making it not sufficient for graduating.

Question 17

A philosopher says, "Studying philosophy is sufficient to teach critical thinking." Which would be the best response if you wanted to argue that this statement was false?
A) "Other disciplines, like literature or science, are just as good at teaching critical thinking."
B) "Other disciplines, like literature or science, also teach very important skills."
C) "Other disciplines, like literature or science, are also necessary for teaching critical thinking."
D) "Other disciplines, like literature or science, could also be sufficient for teaching critical thinking."

Accepted Answer

The answer of A philosopher says, "Studying philosophy is sufficient...

Question 18

"Practicing is necessary if you want to play guitar well." Which of these would be the best response if you wanted to prove that this statement is false? (Pretend for a minute that it's false.)
A) Talent is also necessary if you want to play well.
B) Some people play well even though they have never practiced.
C) Some people learn to play faster than others.
D) Some people never learn to play well even though they practice.

Accepted Answer

B directly challenges the necessity of practice by providing an example where practice is not a factor in achieving the desired outcome (playing guitar well), thus proving the statement false under the given premise.

Question 19

A job ad says, "Qualified candidates for this job must speak fluent Latin." This means that
A) Speaking Latin is sufficient for getting the job.
B) Speaking Latin is necessary for getting the job.
C) Speaking Latin is necessary and sufficient for getting the job.
D) Speaking Latin is neither necessary nor sufficient for getting the job.

Accepted Answer

Being fluent in Latin is a requirement for the job, indicating it's necessary, but the ad does not imply it's the only requirement (sufficient).

Question 20

If a college degree is a necessary condition to be hired for a certain job, then
A) The degree cannot, logically, be a sufficient condition for being hired.
B) The degree must, logically, be a sufficient condition for being hired.
C) If you have the degree, you will definitely get the job.
D) If you don't have the degree, you definitely won't get the job.

Accepted Answer

A necessary condition means that without the degree, you cannot be hired, making option D correct. However, having the degree alone does not guarantee being hired, so it is not a sufficient condition.

Quiz 2: The Elements of Argument

If A is sufficient for B, then B is necessary for

Being at least eighteen is a necessary condition for voting in the United States.

Being a rectangle with four equal sides is necessary and sufficient for being a square.

The presence of oxygen is a sufficient condition for a candle to be burning.

A candle burning is a sufficient condition for the presence of oxygen.

If one state affairs, A, is a necessary condition for another state of affairs, B, then

If A is a sufficient condition for B, then B is

For a human to live, being able to breathe is

For a rectangle to be considered a square, having four sides of equal length is

To be a college student, owning a computer is

For a shape to be a triangle, having three sides is

For winning a race, crossing the finish line first is

"You can't be a good athlete without studying ballet." Which of these would be the best way to prove that this statement is false?

Claim: "Caring about students is a necessary condition for being a good teacher." Objection: "Lots of people care about students and still aren't good teachers." Does this objection show that the claim is wrong?

A certain college requires all students to have physical education credits to graduate. For this college, physical education is

A college offers an elective course in the history of philosophy. Students may choose to take it to fill a humanities requirement or they make take a different course. For this college, the history of philosophy course is

A philosopher says, "Studying philosophy is sufficient to teach critical thinking." Which would be the best response if you wanted to argue that this statement was false?

"Practicing is necessary if you want to play guitar well." Which of these would be the best response if you wanted to prove that this statement is false? (Pretend for a minute that it's false.)

A job ad says, "Qualified candidates for this job must speak fluent Latin." This means that

If a college degree is a necessary condition to be hired for a certain job, then