Results 1 to 2 of 2

Thread: Proof Of Set

  1. #1
    Jan 2010

    Proof Of Set

    For all sets X,Y and Z, prove that if X⊆Y, then
    (i) X ∩ Z ⊆ Y ∩ Z
    (ii) X ∪ Z ⊆ Y ∪ Z
    The problem should be solved in indirect proof way. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Dinkydoe's Avatar
    Dec 2009
    (i) Observe that since $\displaystyle X\subseteq Y$ this means $\displaystyle X = X\cap Y$. Now by using the above observation you want to show the implication:

    $\displaystyle x\in X\cap Z \Rightarrow x\in Y\cap Z$

    (ii) Same trick.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 15
    Last Post: Jun 8th 2011, 11:13 AM
  2. Replies: 5
    Last Post: Oct 19th 2010, 10:50 AM
  3. [SOLVED] direct proof and proof by contradiction
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: Feb 27th 2010, 10:07 PM
  4. Proof with algebra, and proof by induction (problems)
    Posted in the Discrete Math Forum
    Replies: 8
    Last Post: Jun 8th 2008, 01:20 PM
  5. proof that the proof that .999_ = 1 is not a proof (version)
    Posted in the Advanced Applied Math Forum
    Replies: 4
    Last Post: Apr 14th 2008, 04:07 PM

Search Tags

/mathhelpforum @mathhelpforum