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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


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    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.
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