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I'm not a native speaker. Apologies if the question is obvious.

The scenario is:

  • I'm not doing A, and
  • I'm not doing B.

In order to communicate this joint event in a single sentence: should I say: "I'm not doing A or B" or "I'm not doing A and B." (I know I can also say "I'm doing neither A nor B" but that is a seperate solution.)

The source of my uncertainty is that the logical negation of (A and B) is [(not A) or (not B)] so I don't know whether "I'm not doing A and B" can be interpreted as

  • I'm not doing A, or
  • I'm not doing B.

which is not my original scenario.

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    First of all, English is definitely not a logical language. 8^) That said, I think it depends on context. If you're not going to do either of them (either separately or together), I would use "or". If, on the other hand, you're not doing them as a set, I would use "and". Note, however, that this leaves open the possibility of doing one of them alone. E.g., "I'm not eating raw meat or moldy bread!" and "I'm not giving you cake and pie!"
    – Roger Sinasohn
    Commented Jul 17, 2018 at 23:32
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    On the other hand, if you just want to tell people what you're not doing, as in "Guess what I'm doing right now!" "What?" "Well, I'm not making paper dolls or building a model boat!", I would go with "or".
    – Roger Sinasohn
    Commented Jul 17, 2018 at 23:34

1 Answer 1

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The negation of both is:

I am not doing A or B.

If you use and, it just means that they aren't both being done. But it could be that neither is being done, or that only one or the other is being done.

In symbolic logic, the negation of a conjunction is represented by something called De Morgan's Laws. (As at the website Brilliant.)

In brief:

Not (A and B) is the same as Not A or Not B.
Not (A or B) is the same as Not A and Not B.

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  • I agree. Thanks for the reassurance. Will tick when the system lets me to.
    – yurnero
    Commented Jul 17, 2018 at 23:35
  • Love the logical operator example.
    – Ash
    Commented Jul 18, 2018 at 0:17

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