Must and can’t

We use must to say that we feel sure something is true:

You’ve been travelling all day. You must be tired. ( Travelling is tiring and you’ve been travelling all day, so you must be tired.)

We use can’t to say that we feel sure something is not possible:

You’ve just have lunch. You can’t be hungry already. (People are not normally hungry just after eating a meal. You’ve just eaten, so you can’t be hungry. )

Brian said he would definitely be here before 9.30. It’s 10 o’clock now and he’s never late. He can’t be coming.

They haven’t lived here for very long. They can’t know many people.

Study the structure:

                           must     be (tired / hungry / at work etc. )

I /you /he (etc.)               be (doing /coming /joking etc. )  

                           can’t     do / go / know / have etc.

For the past we use must have done and can’t have done:

The phone rang but I didn’t hear it. I must have been asleep.

Jane walked past me without speaking. She can’t have seen me.

Study the structure:

                             must            been ( asleep / at work etc. )

I / you / he (etc.)            have   been ( doing / working etc.)

                             can’t             done / gone / known / had etc.

Couldn’t have… is possible instead of can’t have…:

She couldn’t have seen me.

Tom couldn’t have been looking where he was going.