Results 1 to 3 of 3

Math Help - Need help on a Set Theory proof

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    7

    Need help on a Set Theory proof

    This one must be easy, but I missed the class and we don't have a textbook and I'm just not sure how to approach it. Here goes:

    Prove that for all sets A: A \cap \emptyset = \emptyset

    We've been proving these by converting them into a sort of logical form (i.e. A intersects B turns into (x in the domain of A ^ x in the domain of B). Any suggestions?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2009
    Posts
    57
    Perhaps prove by contradiction? Here's something to get you started:

    Suppose, for the sake of contradiction, that A \cap \emptyset \neq \emptyset. Then there exists x \in A such that x \in \emptyset. However, x cannot be an element of the empty set, because the empty set has no elements. Contradiction.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    Quote Originally Posted by mxrider530 View Post
    This one must be easy, but I missed the class and we don't have a textbook and I'm just not sure how to approach it. Here goes:

    Prove that for all sets A: A \cap \emptyset = \emptyset

    We've been proving these by converting them into a sort of logical form (i.e. A intersects B turns into (x in the domain of A ^ x in the domain of B). Any suggestions?
    A \cap \emptyset = \{x \in A : x \in \emptyset\}

    Assume A \cap \emptyset \neq \emptyset. Then, there must be some element x_0 \in (A\cap \emptyset) \Rightarrow x_0 \in \emptyset \Rightarrow \emptyset \neq \emptyset and therefore that is a contradiction.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: October 19th 2010, 10:50 AM
  2. set theory proof
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: February 25th 2010, 06:11 PM
  3. A Set Theory Proof
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: November 1st 2009, 02:53 PM
  4. Set Theory Proof
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: March 11th 2009, 04:58 PM
  5. Set theory proof help
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: February 12th 2008, 02:33 PM

Search Tags


/mathhelpforum @mathhelpforum