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Can, can't, can't have been etc...

hirashin

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Dear native English speakers,
I need your help. Would you please check my sentences again?
1 Can that rumor be true?
2 In summer, Kyoto can be/become/get hotter than Singapore.
3 Can such a thing happen again?
4 Helen can't be in Spain because I saw her driving past my house this morning.
5 Mike is poor at math/maths. He can't have solved this problem.
6 It's Saturday today. She can't have gone to school.
7 Can that story be true?
8 What he said can't be true.
9 Kyoto can get/be/become very hot.
10 You can't have seen Tom this morning. He is in China now.
11 It can snow even in Kagoshima.
12 He can't have said such a thing.

Thanks in advance.
Hirashin
 
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They all seem fine to me. On number 5 I would phrase it, "Mike is bad at math.". Maths is not correct, mathematics is the correct term. As far as I know poor could be correct in that context I prefer bad though.
 

hirashin

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Thanks for the help, OoTmaster. I appreciate it.
I think British people would use "maths" instead of "math".
OK, I'll replace "poor" with "bad".
Hirashin
 

nice gaijin

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The use of "poor" and "maths" in #5 are not incorrect if you're speaking British English, but Americans wouldn't phrase it that way and may presume to say it's wrong.

However, in the sentences that use "can't have," if I were speaking I would say "couldn't have." I'm not sure I could explain exactly why, but maybe because "can't have done" mixes tenses, whereas "couldn't have done" puts both the action and their presumptive inability to do it in the same time frame.

Perhaps it makes more sense to use "can't" when the reason is an ongoing state or fact. You could get away with either can't or couldn't in either case and not necessarily raise any red flags.
He can't have eaten the steak, he's a vegetarian.
He couldn't have driven home that night, I took his car keys.
 
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Thanks for the help, OoTmaster. I appreciate it.
I think British people would use "maths" instead of "math".
I have always used 'math' in this context, although I have heard 'maths' being used, but it shouldn't be so. 'Math' is the correct way of saying it.
 
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