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Does "does not achieve x and y" equal "achieve neither x nor y"?

English Language & Usage Asked by Jordano on February 27, 2021

Consider the following three statements:

  1. “If Tenant does not achieve x and y then Tenant may terminate the lease.”

  2. “If Tenant achieves neither x nor y then Tenant may terminate the lease.”

  3. “If Tenant fails to achieve both x and y then Tenant may terminate the lease.”

The goal is to only allow Tenant to terminate the lease if they fail at x and fail at y.The situation we want to avoid is Tenant succeeding at one but failing at the other, and therefore claiming “I did not achieve x and y, I only achieved x. Therefore, since I did not achieve both x and y, I may terminate the lease.”

Sentence #1 is the current wording in the lease. I am arguing that it needs to be changed to sentence #2, as that is the only wording where no counterargument could be made that achieving one or the other is grounds for lease termination. I am not sure if sentence #3 works or not, but it seems less bulletproof than sentence #2 to me.

Which sentence(s), if any, achieve the stated goal?

3 Answers

I believe that "neither x nor y" is least ambiguous way to express it concisely.

However, an even clearer way to say it would be to give up on conciseness:

If Tenant fails to X and also fails to Y, Tenant may terminate the lease.

If you had more than 2 or 3 conditions, you could express them as a list, something like:

If Tenant fails to achieve each of the following conditions, Tenant may terminate the lease:

  1. A
  2. B
  3. ...

However, as someone mentioned in the comments, for legal documents your best bet is to consult a lawyer. There's often specific terminology that has become customary. Leases like yours are probably not unique, and there's almost certainly precedent for language that should be used.

Answered by Barmar on February 27, 2021

From a logical perspective, the answer is no. They are not equivalent.


Does not achieve X and Y.

This statement is true if any of the following results occur:

  1. Only X is achieved.
  2. Only Y is achieved.
  3. Neither X nor Y is achieved.

But here is your second statement:

Achieves neither X nor Y.

This is only true in the third result listed above.

If the first or second result occurs, then does not achieve X and Y will be true—but achieves neither X nor Y will be false.

Therefore, your two statements are not logically equivalent.


For further clarification, in order for the logical nor to evaluate to "truth," the conditions on both its sides must evaluate to "false."

Or (as per Wikipedia):

In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both of p and q are false.

Answered by Jason Bassford on February 27, 2021

Logicians like things to be clear and succinct, but the English language was not designed by logicians. It is still being developed as it has been for the last 1000 years by a committee of over 1,000,000,000 people, most of whom have no understanding of logic. If you want to be clear, you may have to forego a little succinctness and add a couple of words:

  1. If Tenant does not achieve x and does not achieve y then Tenant may terminate the lease.

Answered by David Robinson on February 27, 2021

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