Syllogism

About Syllogism

A syllogism question gives two statements and two conclusions, and asks which conclusions must be true whenever the statements are. A conclusion follows only if it holds in every situation the statements allow, which is not the same as being plausible, and not the same as fitting the first example that comes to mind.

What you need to understand

A conclusion follows only if it is true in every situation the statements allow. One situation where it fails is enough to rule it out.

All A are B means every A is a B. It does not say that every B is an A.

Some A are B and Some B are A say the same thing, because the two terms overlap either way.

No A are B also means No B are A. The two are one statement, not two.

Some A are not B is not the same as No A are B. The first allows the rest of A to be B as well; the second forbids any overlap.

A statement about a term says something only if that term has members, so the terms are treated as naming classes with at least one member.

Two statements that contradict each other leave no situation standing, and then every conclusion follows for no good reason. A fair question always leaves at least one situation.

How to work through these questions

Read both statements and note which terms actually appear in them.

Draw the smallest picture that satisfies both statements.

To reject a conclusion, look for one situation that satisfies the statements and breaks it. That is all it takes.

To accept a conclusion, satisfy yourself that no such situation exists, checking each possible way the terms can overlap.

Watch for conclusions that swap the two terms of a statement, since All A are B does not give All B are A.

Decide I and II separately, then combine the two verdicts into one option.

Mistakes that cost marks

Taking All A are B to mean All B are A.
Confusing Some A are not B with No A are B. The first allows overlap, the second forbids it.
Accepting a conclusion because it fits one arrangement, when another arrangement satisfies the statements and breaks it.
Rejecting a conclusion without looking for the situation that would break it.
Treating Some A are B as though it named particular members, when it only says the two classes overlap.
Supposing a term has no members, which makes statements about it vacuously true and conclusions follow for the wrong reason.

Worked example

Statements: All sarvins are melops. Some melops are tanors. Conclusions: I. Some sarvins are tanors. II. Some tanors are melops.

All sarvins are melops, so everything that is a sarvins lies inside melops.
Some melops are tanors, so melops and tanors overlap, but that overlap may lie outside sarvins.
For conclusion I, take a situation in which the sarvins are melops that are not tanors, and the tanors overlap melops elsewhere. Both statements still hold and no sarvins is a tanors, so I does not follow.
Conclusion II says only that tanors and melops overlap, which is what the second statement already says with the terms written the other way round, so II follows.

Answer: Only conclusion II follows

Practice questions with answers

A few Syllogism questions with the full solution shown, so you can see how the method is applied before you attempt the timed set.

Question 1

Two statements are followed by two conclusions. Taking the statements to be true, decide which of the conclusions logically follows. Statements: All dweks are zentas. No dweks are grends. Conclusions: I. All zentas are grends. II. Some grends are not dweks.

A Both conclusions I and II follow
B Neither conclusion I nor II follows
C Only conclusion I follows
D Only conclusion II follows

Answer: Option D — with explanation

A conclusion follows only if it is true in every arrangement allowed by the statements, not merely in the one that comes to mind. Enumerating the arrangements shows that conclusion II holds in every situation the statements allow, while the other fails in at least one. Common mistakes - judged the conclusion from a single arrangement rather than all of them: Both conclusions I and II follow - judged the conclusion from a single arrangement rather than all of them: Neither conclusion I nor II follows - judged the conclusion from a single arrangement rather than all of them: Only conclusion I follows

Question 2

Two statements are followed by two conclusions. Taking the statements to be true, decide which of the conclusions logically follows. Statements: No harkets are murnops. All jorils are harkets. Conclusions: I. Some jorils are harkets. II. Some murnops are not harkets.

A Only conclusion II follows
B Both conclusions I and II follow
C Only conclusion I follows
D Neither conclusion I nor II follows

Answer: Option B — with explanation

A conclusion follows only if it is true in every arrangement allowed by the statements, not merely in the one that comes to mind. Enumerating the arrangements shows that both conclusions hold in every situation the statements allow. Common mistakes - judged the conclusion from a single arrangement rather than all of them: Neither conclusion I nor II follows - judged the conclusion from a single arrangement rather than all of them: Only conclusion I follows - judged the conclusion from a single arrangement rather than all of them: Only conclusion II follows

Question 3

Two statements are followed by two conclusions. Taking the statements to be true, decide which of the conclusions logically follows. Statements: No zentas are vantis. No tanors are vantis. Conclusions: I. Some tanors are not zentas. II. Some vantis are not zentas.

A Neither conclusion I nor II follows
B Only conclusion I follows
C Only conclusion II follows
D Both conclusions I and II follow

Answer: Option C — with explanation

A conclusion follows only if it is true in every arrangement allowed by the statements, not merely in the one that comes to mind. Enumerating the arrangements shows that conclusion II holds in every situation the statements allow, while the other fails in at least one. Common mistakes - judged the conclusion from a single arrangement rather than all of them: Neither conclusion I nor II follows - judged the conclusion from a single arrangement rather than all of them: Both conclusions I and II follow - judged the conclusion from a single arrangement rather than all of them: Only conclusion I follows

Question 4

Two statements are followed by two conclusions. Taking the statements to be true, decide which of the conclusions logically follows. Statements: No murnops are sarvins. No murnops are quorils. Conclusions: I. Some sarvins are not murnops. II. Some murnops are not sarvins.

A Only conclusion I follows
B Both conclusions I and II follow
C Neither conclusion I nor II follows
D Only conclusion II follows

Answer: Option B — with explanation

Question 5

Two statements are followed by two conclusions. Taking the statements to be true, decide which of the conclusions logically follows. Statements: No sarvins are floms. No sarvins are jorils. Conclusions: I. Some jorils are not sarvins. II. Some sarvins are not jorils.

A Both conclusions I and II follow
B Only conclusion II follows
C Only conclusion I follows
D Neither conclusion I nor II follows

Answer: Option A — with explanation

A conclusion follows only if it is true in every arrangement allowed by the statements, not merely in the one that comes to mind. Enumerating the arrangements shows that both conclusions hold in every situation the statements allow. Common mistakes - judged the conclusion from a single arrangement rather than all of them: Only conclusion II follows - judged the conclusion from a single arrangement rather than all of them: Only conclusion I follows - judged the conclusion from a single arrangement rather than all of them: Neither conclusion I nor II follows

Frequently asked questions

What does it mean for a conclusion to follow?

It must be true in every situation the statements allow. If you can describe even one situation that satisfies the statements and breaks the conclusion, the conclusion does not follow.

Does All A are B imply All B are A?

No. Every A being a B leaves room for Bs that are not As, and the reverse statement needs its own justification.

Are Some A are B and Some B are A the same?

Yes. Both say the two classes overlap, and overlap has no direction.

Is Some A are not B the same as No A are B?

No. Some A are not B says at least one A lies outside B and allows the rest to be inside. No A are B forbids any overlap at all.

What happens if the two statements contradict each other?

Then no situation satisfies them, every conclusion becomes vacuously true, and the question has no honest answer. A well-formed question always leaves at least one situation standing.