Is it correct to say "if ... or not"?
My grammar book says only "whether"can be used with"or not","if"cannot.But I seem to have heard some Americans say that(on casual occasions).Is it technically correct or not?
and sentences like"It depends on if he comes tmr or not.","I don't care if he likes me or not...".Do they sound correct?Thanks.

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Those sound fine!  Does your book give an example of how "whether" is used instead of "if"?

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Thank you

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Sorry: They are both wrong. Believe your book.
"I don't care if he likes me or not." may even be common , perhaps especially in American, but it is still wrong grammatically.
If my daughter said either, I would correct her hoping that the incorrect pattern does not get reinforced.
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(New Zealand English native, close to British English)