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Q: Let A be the set of English words that contain the letter x, and let B be the set of English words that contain the letter q. Express each of these sets as a combination of A and B.

(d) The set of English words that do not contain either an x or a q.

The answer in the textbook is: $\bar{A} \cap \bar{B}$

But I got a different answer which is $(A \cap B)^{c}$

because the set contains all the English words except for those that contain both x and q. For example, the word "experience" is in this set because it does not contain q.

Which one is correct?

Alex
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Eric
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    Assuming $\overline{A}$ means $A^c$, the textbook is correct.

    The discrepancy seems to rest on your understanding of the English phrase. It seems like you're interpreting "do not contain either an x or a q" to mean "don't contain an x OR don't contain a q". But I think most people would interpret that phrase to mean the same as "contains neither an x nor a q"

     – Eli Johnson Oct 12 '23 at 00:54
  • The reason why I thought "do not contain either an x or a q" as "don't contain an x OR don't contain a q" is simply because I thought the textbook would use the phrase "neither nor" if the intended meaning is "do not contain x and q". Anyway, I understood your explanation. Thank you for helping me! – Eric Oct 12 '23 at 12:04

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