Statement and Conclusion / Assumption

What is the question?

You get one to three statements. Then you get two conclusions.

You decide which conclusion follows, using only the statements.

What does “follows” mean?

A conclusion follows only if it must be true every time the statements are true.

If it is merely possible or likely, it does not follow.

What must you ignore?

Ignore what you know from real life. A statement may say all cats are tables.

Treat every statement as true, even when it sounds odd.

How do you start?

Turn each statement into a small picture. Use circles for groups.

All means one circle sits inside another. No means two circles stay apart.

How should you treat Some?

Some means at least one. Two circles overlap at least a little.

Some does not tell you the size of the overlap.

Then what?

Test each conclusion against the picture, one at a time.

Mark it follows only if every possible picture agrees.

Why this works: if one allowed picture breaks the conclusion, it is not certain.

Can you see a picture used?

Statement: Some pens are red. Conclusion: All red things are pens.

Draw pens and red overlapping. Red can hold things that are not pens, so the conclusion fails.

Why this works: the picture shows one allowed case where the conclusion is false.

What can you flip?

All A are B does not mean All B are A.

But it does allow Some B are A.

Can you see it solved?

Statements: All pens are tools. All tools are items.

Some items are pens follows. All items are pens does not, because items may include other things.

Why this works: pens sit inside tools, and tools sit inside items. So pens are inside items, and the overlap is real.

Can you chain All and No?

Statements: All birds are animals. No animals are stones.

No birds are stones follows. Birds sit inside animals, and animals stay apart from stones.

Why this works: anything inside animals also stays apart from stones.

Can you join Some and All?

Statements: Some pens are red. All red things are bright.

Some pens are bright follows. The red pens are inside red, and red is inside bright.

Why this works: the overlap you were given stays inside the larger circle.

What about No?

No A are B can be flipped. No B are A follows at once.

It also gives Some B are not A, if B exists.

Why is Some tricky?

Two Some statements do not join up. The overlaps may be in different places.

Some A are B and Some B are C gives no sure link between A and C.

Can you see it solved?

Statements: Some books are files. No files are boxes.

Some books are not boxes follows, because the files that are books are not boxes. No books are boxes does not follow.

Why this works: only the books that are files are known to stay away from boxes. Other books may be boxes.

What is the safe rule?

A Some statement tells you about only the part it names.

Never stretch it to the whole group.

When does either-or apply?

It applies when neither conclusion follows by itself.

The two conclusions must be a yes-and-no pair on the same link.

Can you see it solved?

Statements: Some cups are plates. Some plates are jugs.

Some cups are jugs and No cups are jugs form a pair. One of them must be true, but we cannot say which.

Why this works: the cups and jugs may meet or may not. Both cannot be false at once, so one must be true.

Is the test tricky?

Check for the pair before you answer. Check it only after you have tested each conclusion alone.

If one conclusion already follows, the pair rule does not apply.

What is an assumption?

An assumption is a hidden belief behind a statement. The statement fails without it.

Example: Buy a helmet to stay safe. The assumption is that helmets protect riders.

Can you see another assumption?

Statement: Schools should start yoga classes to improve focus.

Assumption: yoga can improve focus. The statement depends on it.

It does not assume that every child loves yoga.

Why this works: if yoga could not improve focus, the advice would make no sense.

What is a course of action?

It is a step to fix a problem named in the statement.

A good step addresses the problem directly and is practical.

Can you judge two actions?

Problem: Many city roads flood in the monsoon.

Action I: Clear and build drains. That fixes the cause, so it is a good step.

Action II: Close every road all monsoon. That is not practical, so it is a weak step.

Why this works: a good action is both useful and possible.

How do you test them?

For an assumption, ask whether the statement would fall if the idea were false.

For a course of action, ask whether it would really help.

What mistakes cost marks?

Using real-world facts instead of the statements.

Treating a possible conclusion as a certain one.

How do you stay quick?

Draw one small picture per question and test both conclusions on it.

Use the either-or option only as a last step.

How should you practise?

Do five of these a day, and write down why each wrong one fails.

Then try the quiz below and read every explanation.