1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I used the definitions, now what?

  1. Jun 24, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove:

    1. [tex] R \cap ( S \cup T ) = (R \cap S) \cup (R \cap T)[/tex]

    2. [tex] S \cap ( S \cup T ) = S[/tex]

    2. The attempt at a solution

    I suppose this is all about using the definitions, and I eventually get down to this:

    For (1), the LHS is down to x e R and (x e S or x e T), while the RHS is (x e R and x e S) or (x e R and x e T). There's one small leap here, I know. How do I show these two are equivalent?

    For (2), I should show that (x e S) and (x e S or x e T) is equivalent to (x e S). What logical conclusion am I missing here?
     
  2. jcsd
  3. Jun 24, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If nothing else, use a truth table. x is either in or is not in R, S and T. That leaves you eight cases. Four in the second one. Is the logic true in all cases? With some moderate cleverness you don't even have to check all eight. Sure, it's just logic.
     
  4. Jun 24, 2008 #3
    for (2), if x is in the lhs then x is in S and (S or T). So x is in the rhs.
    If x is in the rhs, x is in S and so x is in (S or T). So x is in S and (S or T), so x is in the lhs.

    Thus the lhs is a subset of the rhs and the rhs a subset of the lhs, so the two sets are equal.
     
  5. Jun 25, 2008 #4
    Thanks guys -- that got me on the right track.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?