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Are both the sentences correct?

I don't care whether you're married or single.

I don't care if you're married or single.

When to use whether over if?

  • What research have you done? – BillJ Mar 30 '18 at 10:27
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1) We use whether and not if after prepositions:

*Later I argued with the doctor about whether I had hit my head, since I couldn’t remember feeling it.*

Not: *Later I argued with the doctor about if I had hit my head …*

*The police seemed mainly interested in whether there were any locks on the windows.*
Not: *The police seemed mainly interested in if there were any locks …*

2) We use whether, not if, before to-infinitives:

*I don’t know whether to buy* the blue one or the red one.

3) We use whether, not if, after prepositions:

[talking about a trip to Australia for a year]

We’re not interested in whether we get great jobs and that kind of thing, we just want to have a good time.

4) We use whether, not if, directly before or not:

*Can you tell me whether or not you’re interested in the job.* 

(https://dictionary.cambridge.org/grammar/british-grammar/if-or-whether)

I your case I would use whether or not, e.g.: I do not care whether she is married or not.

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