Logical Deduction

About Logical Deduction

A deduction question gives two statements and asks which conclusion follows from them. Following has a precise meaning: the conclusion must be true in every arrangement that satisfies the statements, not merely in one arrangement you can picture. That distinction is the whole subject, and it is why a conclusion that sounds reasonable can still be wrong.

What you need to understand

"All A are B" places every A inside B. It says nothing about whether every B is inside A.

"No A are B" means the two groups do not overlap at all, so an A can never be a B.

"Some A are B" means at least one A is also a B. It gives no information about how many.

Linking two universals gives a longer chain: if all A are B and all B are C, then all A are C.

A conclusion follows only when it must be true in every arrangement that satisfies the statements. Being possible is not enough.

Reversing the direction of a chain, or upgrading "some" to "all", produces conclusions that do not follow.

How to work through these questions

Write the statements as a chain of groups, one inside the next.

Join the links where the two statements share a group.

For each option, ask whether it must be true in every arrangement that satisfies the statements.

Reject any option that needs an extra assumption to hold.

Watch for options that reverse the chain, contradict a statement, or convert "some" into "all".

Mistakes that cost marks

Reversing a universal statement: "All A are B" does not give "All B are A".
Upgrading "some" to "all", or to "no", which changes the meaning completely.
Accepting a conclusion that is possible rather than one that is certain.
Forgetting that a negative statement breaks the chain, so nothing beyond it can be concluded.
Letting knowledge of the real world override what the statements actually say.

Worked example

All roses are flowers. All flowers are plants. Which conclusion follows?

Put the groups in a chain: roses sit inside flowers, and flowers sit inside plants.
Join the two links, so roses sit inside plants.
Test the reverse: not every plant is a flower, so the chain cannot be read backwards.
The conclusion that all roses are plants must be true, so it follows.

Answer: All roses are plants.

Practice questions with answers

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

Question 1

Read the statements and decide which conclusion follows. All Poldal are Frelfrel. All Frelfrel are Torwob.

A No Poldal are Torwob.
B All Poldal are Torwob.
C Some Poldal are not Torwob.
D All Torwob are Poldal.

Answer: Option B — with explanation

Everything that is Poldal is also Frelfrel, and everything that is Frelfrel is also Torwob. Joining the two links gives: all Poldal are Torwob. The reverse (Torwob therefore Poldal) does not follow, and the remaining options contradict the statements. Common mistakes - contradicts the statements outright: No Poldal are Torwob. - reversed the direction of the chain: All Torwob are Poldal. - contradicts the statements outright: Some Poldal are not Torwob.

Question 2

Read the statements and decide which conclusion follows. All Torfen are Wobpol. No Wobpol are Trudal.

A No Torfen are Trudal.
B All Trudal are Torfen.
C Some Torfen are Trudal.
D All Torfen are Trudal.

Answer: Option A — with explanation

Every Torfen is a Wobpol, and nothing that is Wobpol is a Trudal. Since each Torfen is a Wobpol, no Torfen can be a Trudal. So no Torfen are Trudal, and the options that assert some overlap contradict the second statement. Common mistakes - contradicts the second statement: Some Torfen are Trudal. - contradicts the second statement: All Torfen are Trudal. - reversed a chain that is already broken: All Trudal are Torfen.

Question 3

Read the statements and decide which conclusion follows. Some Wobmel are Kanblo. All Kanblo are Raznix.

A No Wobmel are Raznix.
B All Raznix are Wobmel.
C Some Wobmel are Raznix.
D All Wobmel are Raznix.

Answer: Option C — with explanation

It is given that some Wobmel are Kanblo, so take one of those. It is a Kanblo, and every Kanblo is a Raznix, so it is a Raznix. That gives at least one Wobmel that is a Raznix: some Wobmel are Raznix. It would be wrong to generalise that to all Wobmel. Common mistakes - generalised from 'some' to 'all': All Wobmel are Raznix. - reversed the direction of the chain: All Raznix are Wobmel. - contradicts the statements: No Wobmel are Raznix.

Question 4

Read the statements and decide which conclusion follows. All Nixpol are Tormel. All Tormel are Frelmel.

A All Nixpol are Frelmel.
B No Nixpol are Frelmel.
C Some Nixpol are not Frelmel.
D All Frelmel are Nixpol.

Answer: Option A — with explanation

Everything that is Nixpol is also Tormel, and everything that is Tormel is also Frelmel. Joining the two links gives: all Nixpol are Frelmel. The reverse (Frelmel therefore Nixpol) does not follow, and the remaining options contradict the statements. Common mistakes - reversed the direction of the chain: All Frelmel are Nixpol. - contradicts the statements outright: Some Nixpol are not Frelmel. - contradicts the statements outright: No Nixpol are Frelmel.

Question 5

Read the statements and decide which conclusion follows. All Kanmur are Quenpol. No Quenpol are Murlaz.

A Some Kanmur are Murlaz.
B All Murlaz are Kanmur.
C No Kanmur are Murlaz.
D All Kanmur are Murlaz.

Answer: Option C — with explanation

Every Kanmur is a Quenpol, and nothing that is Quenpol is a Murlaz. Since each Kanmur is a Quenpol, no Kanmur can be a Murlaz. So no Kanmur are Murlaz, and the options that assert some overlap contradict the second statement. Common mistakes - contradicts the second statement: Some Kanmur are Murlaz. - contradicts the second statement: All Kanmur are Murlaz. - reversed a chain that is already broken: All Murlaz are Kanmur.

Frequently asked questions

What does "follows logically" mean here?

It means the conclusion is true in every arrangement that satisfies the two statements. A conclusion that is merely possible, or true in one arrangement you happen to picture, does not follow.

Why is "All B are A" wrong when all A are B?

Because the statements only put A inside B. There may be members of B that are not A, so claiming every B is an A adds something the statements never said.

How do I handle a statement that begins with "some"?

Treat it as saying at least one exists, and nothing more. You may use that one member to build a conclusion, but you can never generalise from "some" to "all".

What does a negative statement do to the chain?

It stops it. If no B are C, then anything shown to be a B is definitely not a C, and no further link can be made through C in the positive direction.

Can more than one conclusion follow from the same statements?

It is possible in principle, but questions are written so that exactly one of the given options must be true. If two of the options both seem to hold, re-read the statements, because one of them usually needs an assumption.