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!

Sets and functions, theoretical calc homework?

  1. Jan 26, 2014 #1
    1. The problem statement, all variables and given/known data
    Let A,B, and C be subsets of universal set U. Prove the following
    A. If U=A union B and intersection of A and B is not an empty set, then A= U\B
    B. A\(B intersection C) = (A\B) union (A\C)


    2. Relevant equations

    no relevant equations required

    3. The attempt at a solution
    A.
    So I know A union B = {x: (xεA) or (xεB)}
    But I am having trouble on where to go from there. Intuitively I can see that the claim is true, but how do I prove this? step by step please

    B.
    I know that B intersection C= : {x: (xεB) and (xεC)}
    A\B = {x: (xεA) and ~(xεB)}
    A\C = {x: (xεA) and ~(xεC)}
    Same problem as part a how do I prove this?
     
  2. jcsd
  3. Jan 26, 2014 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Hello concon,

    Welcome to PF !

    We don't do step by step solutions here at PF, if that's what you're asking for.

    It looks to me that A is not true.


    In general, to show that two sets are equal, i.e. D = E, show that D is a subset of E and E is a subset of D.
    To show that set D is a subset of E:
    Let xεD. Then show that it follows that xεE .
    etc.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Sets and functions, theoretical calc homework?
  1. Set theoretic problems (Replies: 1)

Loading...