A question in my text book for a course I'm taking over winter is asking me to give the set builder notation for (X∪Y)' [i.e. the complement of the union of set X and set Y] given that U=Z^+ [i.e. the universal set is that of all positive integers], X={1,2,3,4,5}, and Y={2n | n ∈ Z^+} [i.e. all positive even integers]. Basically, I'm looking for the set builder notation for the compliment of {1,2,3,4,5,6,8,10,12,14,...}.
I've figured out that the complement is {7,9,11,13,15,17,...}, or all positive odd integers greater-than or equal-to 7.
The issue is that the textbook doesn't give a very clear explanation as to what is and isn't correct when writing set builder notation. I've searched the internet for explanations and examples, but I've just been getting a lot of vague and/or conflicting information that doesn't tell me whether I've got the right set builder notation.
The answer that I have is (X∪Y)' = {n ∈ Z^+ | 2n+1 ≥ 7}.
Can someone tell me if this is correct? Or how I should change it if it isn't? Thank you in advance!