The union of a subset and its complement

[chipotleaway]

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.

 

[FactChecker]

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"

 

[chipotleaway]

Haha appropriate username, thanks. How come this isn't mentioned in most books? Seems like all the 'obvious' stuff is.