Modal verbs and their negatives

positive

negative

must (used for a personal opinion)
He must be crazy.

can't
He can't be crazy.

must / have to / has to (used for obligation)
You must arrive by 8 o'clock.
You have to arrive by 8 o'clock.

don't have to / needn't = something is not necessary
You don't have to arrive by 8 o'clock.
You needn't arrive by 8 o'clock.

can (used for ability)
I can play the guitar.

can't / cannot
I can't play the guitar.

can (used for possibility)
You can smoke here.

can't / cannot / mustn't
You can't smoke here.
You mustn't smoke here.