That man mustn't be Tom's father

Hello, native English speakers,
Would you help me with English again?

(a) I haven't heard Molly moving about. She mustn't be awake yet. Her
alarm mustn't have gone off.

(b) I haven't heard Molly moving about. She can't be awake yet. Her
alarm can't have gone off.

According to Michael Swan's Practical English Usage, American people sometimes
use (a) instead of (b). Is that right?

Then, would both (c) and (d) also sound right?
(c) It mustn't be the postman at the door. It's only seven o'clock.
(d) That man mustn't be Tom's father. He doesn't look like Tom at all.

Thanks in advance.

Hirashin

Americans don't use mustn't. (contraction) Especially not two times in a row in such short sentences.

In (a), second sentence should be must not. Third would then not repeat must. Instead, her alarm probably didn't go off.

(b) Second sentence, something similar, she must not be awake yet. Her alarm probably didn't go off./Maybe her alarm didn't go off.

(c) and (d), I'd use can't instead of mustn't in both cases.

Thanks for the help.
I'm surprised to hear Americans don't use mustn't.
Hirashin