# Any of four combinations are true? "Both X and Y are A or B" could be wrong?

I want to write a sentence to mean that any of the following 4 situations are true.

1. X = A and Y = A,
2. X = B and Y = B,
3. X = A and Y = B,
4. X = B and Y = A.

The following sentence,

Both are A or B.

means only the first two cases in the list above. In other words,

Both X and Y is A or both X and Y is B.

So, I could write a sentence,

X is A or B and Y is A or B.

Am I right, or is there a better or concise way of writing a sentence for meaning that any of 4 situations are true?

P.S. Please, edit tags for this question if needed. I am not sure what tags are appropriate for this kind of question.

• I would say each of X and Y can be whether A or B.
– Nate
Sep 15, 2013 at 20:34
• Whether strikes me as strange. I would use either instead. But other than that I agree with Nate. Sep 15, 2013 at 21:11
• Thank you for your answer. Nate might think that either A or B was a sentence. Because I considered A or B as words, either is a correct choice. Thank you again. Sep 15, 2013 at 21:15
• Combining thoughtful answers from Pam, Nate, and RegDwighт, I could write a sentence Each of A and B is either X or Y. to mean that any of four combinations are true. Thank you all for your answers. Sep 15, 2013 at 21:20

I'd say, X and Y can take any value A or B.

• Thank you for the answer. It is better than joining two sentences. Sep 15, 2013 at 20:28
• Would you agree that Both are A or B. refers to only the first two cases in the list of 4 possibilities? I also want to know whether the sentence Both are A or B. is the same in meaning as the sentence you suggested. Sep 15, 2013 at 20:30
• I would agree. So, it should not the same meaning as my sentence. But wait for a native speaker confirmation too. :-)
– Pam
Sep 15, 2013 at 20:40

I would write

X and Y can be either A or B.

For example:

Dogs and cats can be either male or female.

• Thank you for your answer. I like the simpler form without Each of. It seems ambiguous to me. When it is clear from the context, I would like to use your choice of the sentence, though. Sep 16, 2013 at 2:23

Perhaps

Both are either A or B.

• Thank you for the answer. Is it ambiguous? The sentence, "Both are either A or B." seems to mean that only the first two cases of the four cases are true. I am not sure, though. I more like "Each of X and Y" than just Both. But, thank you for your thought. Sep 16, 2013 at 1:34
• I agree. The shortest form is Each are either A or B, or even Each are A or B.
– bib
Sep 16, 2013 at 2:06
• Thank you!!! I like the simpler form with a slight modification: "Each is either A or B." Sep 16, 2013 at 2:08
• And I stand corrected. Each takes is not are.
– bib
Sep 16, 2013 at 2:31