Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The union of a subset and its complement

  1. Feb 27, 2014 #1
    If S is a subset of X, and cS is the complement of S with respect to X, is the union of S and cS equal to X? Seems like a no-brainer but just want to be sure because I've yet to find a book that comments on this.
  2. jcsd
  3. Feb 27, 2014 #2


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    Yes. You can pick any element of X and prove that it is in the union of S and cS. Use the definition of "complement" and "union"
  4. Feb 27, 2014 #3
    Haha appropriate username, thanks. How come this isn't mentioned in most books? Seems like all the 'obvious' stuff is.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook