Must and Can't for Deduction | B2 Modal Verbs

1. Overview & Concept

What is it? At B2 level, must and can't are used not just for obligation/prohibition but for logical deduction — reaching a conclusion based on evidence.
Purpose: To express that you are almost certain about something because the evidence strongly points to it.
Key idea: Must = logically certain (positive); can't = logically impossible (negative).

Meaning	Structure	Example
Certain deduction (present)	Subject + must + base verb	She must know the answer.
Impossible deduction (present)	Subject + can't + base verb	He can't be serious.
Certain deduction (past)	Subject + must have + past participle	They must have left already.
Impossible deduction (past)	Subject + can't have + past participle	She can't have forgotten.
Continuous (present)	Subject + must be + verb-ing	He must be sleeping.

Rule 1 — Must for near-certain positive deduction: Use must when you are almost certain something is true based on evidence.
You've been travelling for 12 hours — you must be exhausted.
The lights are on — someone must be home.
Rule 2 — Can't for near-certain negative deduction: Use can't when you are almost certain something is impossible or untrue.
He just ate a huge meal — he can't be hungry already.
She studied for weeks — she can't have failed.
Rule 3 — Must have / Can't have for past deductions: When deducing about completed past events.
The door is open — someone must have left it unlocked.
He looks fresh — he can't have been working all night.
Rule 4 — Degree of certainty: The deduction scale runs:
must (95%+ certain) → should (75%) → might/may (50%) → can't (95%+ certain it's NOT true)
Rule 5 — Cannot vs can't: Both are correct; can't is more common in speech.

Signal	Example
Evidence words	look at him, judging by, considering
Reasoning phrases	He works 80 hours a week, so he must…
Contradiction phrases	But she said she was ill — she can't have…

Mistake	Correction	Explanation
She must to be tired.	She must be tired.	No to after a modal.
He mustn't be home. (deduction)	He can't be home.	For negative deduction, use can't, not mustn't.
They must have went.	They must have gone.	After have, use past participle.
She can't to have known.	She can't have known.	No to in modal perfect.

You've been awake since 4 a.m. — you must be exhausted.
He's wearing a winter coat indoors — he must be cold.
She passed every exam with top marks — she can't have found it difficult.
The restaurant is empty — the food can't be very good.
They've been married for 30 years — they must love each other deeply.
He just bought a new Ferrari — he must earn a lot of money.
She didn't answer the phone at midnight — she must have been asleep.
The window is smashed — someone can't have left it like that by accident.
You know six languages? You must have an incredible memory.
They arrived looking completely relaxed — the journey can't have been stressful.

Modal	Use	Certainty	Example
must + base verb	positive deduction (present)	~95%	She must be right.
can't + base verb	negative deduction (present)	~95%	He can't be lying.
must have + pp	positive deduction (past)	~95%	They must have left.
can't have + pp	negative deduction (past)	~95%	She can't have known.
might/may	uncertain possibility	~50%	It might be true.