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Hi. Would you help me with the use of the two modal verbs "would" and "can"?

1. the use of "would"

Would you say the use of the following "would" is conditional? I feel the context given below might not be clear but I hope you could help me.

(a man talking to another person)

Wouldn't this be a sad thing? A man/boy studies hard for a test, and on the test day, he goes and takes the test. And it would be a wrong test.

2. the use of "can"

I can't go swimming today.

I think I have asked a similar question in another thread I started a few days ago, but I wish you could help me further by answering the following questions.

a) Does the modal verb "can" (as in "can't) denote ability?

b) I think I could replace the part "can't go" with the phrase "will not be able to." And whenever we can use the phrase "be able to," are we using it (or suppose to use it) to denote ability?

c) When we use the modal verb "can" and the phrase "is able to," are we encompassing situations that deal with physical ability, like lifting a box, and what I might call "situation-dependent ability" (just made the term up - I think it is likely not to be the correct term), like a person's schedule not permitting one to go swimming, as in the above example sentence "I can't go swimming today"?

Also is this correct?

Our company is in serious debt. Unless we get some help soon, we can't go on.
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Anonymousa man talking to another person)
Wouldn't this be a sad thing? A man/boy studies hard for a test, and on the test day, he goes and takes the test. And it would be a wrong test.
The second "would" (which I assume is the one you're asking about) seems unexpected to me and inconsistent with what has come before. The context seems to call for "And it's the wrong test".
AnonymousWhen we use the modal verb "can" and the phrase "is able to," are we encompassing situations that deal with physical ability, like lifting a box, and what I might call "situation-dependent ability" (just made the term up - I think it is likely not to be the correct term), like a person's schedule not permitting one to go swimming, as in the above example sentence "I can't go swimming today"?
Yes, this seems is a reasonable distinction to make. In "I can't go swimming today", the speaker is talking about the absence of opportunity, not the absence of physical ability. Contrast this with "I can't swim", which talks of physical ability.

The following are more or less equivalent in meaning, but the shorter versions with "can" are more likely in everyday conversation:

"I can't go swimming today" = "I'm not able to go swimming today" = "I won't be able to go swimming today"

"I can't swim" = "I'm not able to swim"
AnonymousAlso is this correct?
Our company is in serious debt. Unless we get some help soon, we can't go on.
This is OK, but strictly speaking I prefer "... we won't be able to go on".
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Thank you for your help.