Results 1 to 3 of 3

Math Help - Sets

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    37

    Sets

    Let A and B be sets. Prove each of the following statements. Remember, using a Venn diagram might help to visualize the problem, but it's not a proof!

    a. (A B) ⊆ A
    b. A ⊆ A ∪ B
    c. A (B - A) = 0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Oct 2008
    Posts
    17
    a) (A B) ⊆ A

    Let x be in (A B), then x is in A and x is in B. Hence x is in A. Thus (A B) ⊆ A

    b) A ⊆ A ∪ B

    This one seems so easy to prove, I'm not sure what else to say about it:

    Let x be in A. If x is in A then x is in A ∪ B. Thus A ⊆ A ∪ B

    c) A (B - A) = 0

    (B - A) = {x | x is in B and x is not in A}. So intuitively this equality should make sense. You take everything that is in A and intersect with everything that is in B takeaway A, so A and (B-A) should be mutually disjoint sets).

    For some reason I can't think of how to prove this one, sorry. Someone else will have to tackle it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2008
    Posts
    39
    Quote Originally Posted by captainjapan View Post
    Let A and B be sets. Prove each of the following statements. Remember, using a Venn diagram might help to visualize the problem, but it's not a proof!

    a. (A B) ⊆ A
    b. A ⊆ A ∪ B
    c. A (B - A) = 0

    a) xε( Α \cap B) <====> (xεA & xεB) ====> xεA.


    b) xεA =====> xεA v xεB <=====> xε( AUB)


    c) xε[A \cap (B-A)] <====> xεA & (xεB & ~xεA) <=====>


    (xεA & ~xεΑ) & xεB <====> xε ( Α \cap A') & xεB <=====> xε( Φ \cap B) <====> xεΦ.


    Because A \cap A' = Φ and , Φ \cap B =Φ

    Φ being the empty set
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Open sets and sets of interior points
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 9th 2011, 03:10 AM
  2. Metric spaces, open sets, and closed sets
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: March 16th 2011, 05:17 PM
  3. Replies: 9
    Last Post: November 6th 2010, 12:47 PM
  4. Approximation of borel sets from the top with closed sets.
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 18th 2010, 08:51 AM
  5. how to show these sets are 95% confidence sets
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: February 11th 2009, 09:08 PM

Search Tags


/mathhelpforum @mathhelpforum