CAN :  We use ‘Can ‘ to say that something is possible or that somebody has the general ability to do something .  ‘ Can ‘ frequently precedes verbs of perception.  Thus it indicates (a) your own ability (b) positive permission (c) perception (d) possibility etc.

• Can you lift this box? (ability)
• You can drive my car.( positive permission)
• Can you hear me well?( perception)
• He can be in the town now.(possibility)
• Children can sometimes be very trying.
• It can be very cold here even in May.
• Can I borrow your pen, please?

Must :

(1)  We use ‘ Must ‘ to say that we feel /assume something.  This is to show our assumption, but when we rule out or deny the probability we should use ‘ Can’t ‘ and NOT ‘ Mustn’t ‘.( Or in other words , in negative sentences we use ‘ can’t ‘ instead of ‘ mustn’t ‘ when we deal with probability aspect)

• You’ve been travelling all day.  You must be tired.
• They have just had lunch.  They can’t be hungry.( We don’t say,  ‘they mustn’t be…)
• He must come before 8 o’ clock.( i.e based on certain assumptions, one is compelled to arrive at the conclusion that he………)
• It is 10 o’ clock  now and he is never late.  He can’t be coming.
• This must be the way, surely.
• This can’t be the way, surely.( We don’t say , ‘ This mustn’t be the way….)
• John has gone to Delhi.  He can’t be back before Friday.
• They haven’t lived here for very long.  They can’t know many people.

(2)  ‘ Must ‘ indicates obligation that is considered inescapable.( here the negative is ‘ mustn’t  ‘)

• You must look after your parents when they are old.
• You mustn’t hurt the helpless creature.
• I told him I must be very frank…..(OR) I told him I had to be……

Note:  The past equivalent of ‘ Must ‘ is  ‘ Had to ‘.  However, in the past reported speech ‘Must’ can be used in place of ‘ Had to ‘.

(3)  Must : when we want or intend to do something fairly soon.

• I must go and make a phone-call.
• I must meet him and convey this message today itself.

(4)  Must :  When we suggest that somebody should do something.

• You are a good writer.  You must publish your works.
• You must come and visit me.