Results 1 to 3 of 3

Math Help - Proof of sets

  1. #1
    Junior Member
    Joined
    Jul 2006
    Posts
    73

    Proof of sets

    I got help with one proof already, I am just lost when it comes to proofs....here is another on...

    Problem:

    Prove that the empty set is unique. That is, suppose that A and B are empty sets and prove that A=B
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by luckyc1423 View Post
    I got help with one proof already, I am just lost when it comes to proofs....here is another on...

    Problem:

    Prove that the empty set is unique. That is, suppose that A and B are empty sets and prove that A=B
    If we are working in the Zermelo-Frankael Set theory model, we will use the axiom of extensionality.
    "Two sets are equal if and only if for any element of A if and only if is an element of B".
    Since A has no elements the statement,
    "If x in A then x in B" is true.
    Similarly,
    "If x in B then x in A" is true.

    These statements are true because the hypothesis of the conditional is false. And a false impling a true of a false impling a true is always true. Thus these statements are both true.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,914
    Thanks
    779
    Hello, luckyc1423!

    Prove that the empty set is unique.
    That is, suppose that A and B are empty sets. .Prove that A=B.
    Here's a rather primitive approach . . .


    Let A = \emptyset and B = \emptyset.

    When are two sets A and B unequal?

    They are unequal if there is an element in A which is not in B
    . . . . . . . . . . .or if there is an element in B which is not in A.

    (1) Is there an element in A which is not in B?
    . . . Since A = \emptyset, the answer is No.

    (2) Is there an element in B whichis ot in A?
    . . . Since B = \emptyset, the answer is No.


    Therefore: . A = B

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof with sets
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 2nd 2011, 10:31 AM
  2. Help with Proof of Sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 20th 2010, 09:25 PM
  3. A sets proof
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: August 25th 2010, 04:47 AM
  4. Proof with sets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 8th 2008, 02:11 AM
  5. Proof - sets
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: January 11th 2008, 04:32 PM

Search Tags


/mathhelpforum @mathhelpforum