1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Proving a set identity

  1. Feb 7, 2014 #1
    1. The problem statement, all variables and given/known data


    2. Relevant equations

    I have to use these set identities:




    3. The attempt at a solution

    Pretty sure this is impossible because there's no identity for the Cartesian product.
  2. jcsd
  3. Feb 7, 2014 #2
    Just go at it the old fashion way.

    Suppose (a, d) [itex]\in[/itex] A X (B [itex]\cup[/itex] C). Then a [itex]\in[/itex] A. Also d [itex]\in[/itex] B or d [itex]\in[/itex] C. So (a,d) [itex]\in[/itex] (A X B) or (a,d) [itex]\in[/itex] (A X C).

    Thus (a,d) [itex]\in[/itex] (A X B) [itex]\cup[/itex] (A X C).

    Therefore A X (B [itex]\cup[/itex] C) [itex]\subseteq[/itex] (A X B) [itex]\cup[/itex] (A X C).

    Proving the subset goes the other way follows similarly.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted