Are these two statements equivalent?

If you don't satisfy either of the conditions A and B

If you don't satisfy both of the conditions A and B

I interpret the "either" case as:

If you fail to meet at least one of A or B.

But the "both" case has me confused when a non-native English speaker questioned me on it. (I'm a native English speaker).

Example of "either" on this page:

To use the self-service application to download and install Office 2016, you’ll need two things:

  • Mac OS X 10.10 (Yosemite)
  • The self-service software application included on L&S-managed Macs

If you don't meet either of those requirements

(Emphasis added)

Example of "both" on this page:

In the second stage of screening if you meet both of the following requirements you don’t need to do any further assessment of that substance. You’ll need to do detailed modelling of emissions that don’t meet both of the following requirements

(Emphasis added)

My opinion is that using "both" to mean "either" is sloppy and confusing, because it seems like "both" should mean:

you fail to meet A and you fail to meet B

In other words, I think that the "both" case doesn't apply to you if you've satisfied at least one.

Is there a "standard" way to read the "both" statement?

  • Both A and B = A + B; Not both A + B = A alone or B alone or neither (none) Jan 9 '17 at 20:07
  • 3
    When you have a negative (don't or fail) and a conjunction (or, and) in the same clause, you are very likely to get ambiguity, because in language negatives, modals, quantifiers, and conjunctions do not always obey De Morgan's laws. Jan 9 '17 at 20:33
  • @JohnLawler I'm not so sure it's an issue with applying De Morgans laws. The problem seems to be more foundational - how to construct the original expression, i.e. whether the negation should initially distribute to the 2 terms (not(A) & not(B)), or apply to the quantity (not(A & B)).
    – Kelvin
    Jan 9 '17 at 20:39
  • 3
    That's one form of De Morgan's Laws; and that's why it's ambiguous -- it's impossible to construct the original expression. Information is always lost with deletion rules, and conjunction reduction has deleted enough structure to lose the trail here. Jan 9 '17 at 20:48

If you don't satisfy both of the conditions A and B means it doesn’t matter what happened to the other; at least one of conditions A or B was not met.

If you don't satisfy either of the conditions A and B is confused by the use of and with either. In every-day English there might be a tiny difference at worst but as soon we enter any specialised territory the ice thins and A and B would be better described as A or B

  • Too right, Lawrence. What could I have been thinking? Thanks for pointing that out. Jun 21 '17 at 21:32

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