Question: I heard this sentence in an American film a while ago as I was watching it on DVD (the part after **but** is verbatim):

*"I'm doing my best but **I mustn't be doing it right**."*

This is something I occasionally hear in American films: phrases like *"he mustn't have done it"* or *"she mustn't be studying now"*, where a logical conclusion is expressed. So far I've thought that the normal thing to say is *"he can't have done it"* or *"she can't be studying now"*.

My question is: Can **mustn't** be used to express a logical conclusion when the speaker is certain that something didn't happen or isn't happening, at least in informal speech? Is this an American usage? (I've never heard this usage in British English, but this doesn't mean it doesn't exist.) Is there a change going on in the usage of the particular modal verb?

Note: All the references I've checked don't even mention this use of **mustn't**. Google books aren't of help either. 

EDIT: I should clarify that I'm asking this question because if I wanted to express that I'm certain I'm not doing something right (as in the sentence quoted from the film) I'd say *"I'm doing my best but I **can't** be doing it right"*. I would think that the use of **mustn't/must not** wouldn't be standard usage (although the meaning is perfectly clear to me; I never mistook it for an injuction).

Answer: 
Several replies here address whether it is appropriate to use the contraction "mustn't" rather than writing out "must not" in such an example. Is this your question, or are you asking about the definition of the word "must"? Assuming the latter ...

"Must" can mean "obligated, required", as in, "You must pay your taxes by April 15", or "You must be quiet while the teacher speaks." That definition doesn't make sense in this context. But "must" can also mean "compelled by necessity, inevitable", as in, "If you hold a rock in the air and release it, it must fall to the ground". The rock is not compelled to fall by the laws of the state legislature, but by the laws of physics.

That's the sense in which "must" is used in contexts like your example. "If A is true, then B must be true" means that B follows inevitably from A because of laws of nature or mathematics or logic. "If the engine is getting fuel, then the problem must be in the electrical system." "Must" here doesn't mean that the problem had better start being in the electrical system or we will subject it to public ridicule or have it arrested. It means that it is (or at least, the writer believes it to be) a logical inevitability.
When considered deductions, **can’t be** or **can’t/couldn’t have been** is negative of **must be**. 

**Mustn't be** is also negative of **must be** meaning that there is no possible way that it could be otherwise. It implies the certainty of the speaker's own claim.

Please compare:

> 
> a) ... but I must be doing it **wrong**.  
> 
>  b) ... but I can't be doing it **right**. 
> 
> 
> a) ... but I must be doing it **wrong**.  
> 
>  b) ... but I must't be doing it **right**. 
> 
> 
> 

**Edit 1**

Irene, with reference to your sentence

> 
> ... I'd say "I'm doing my best but I can't be doing it right".
> 
> 
> 

To construct the sentence in this way, the sentence in question should have been "I'm doing my best but I **must be** doing it **wrong**.

Think about how the words "right" and "wrong" contribute to "deduction" together with "must be", "mustn't be", "can't be".