Results 1 to 3 of 3

Math Help - subset help

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    66

    subset help

    I need to prove that A is a subset of B if and only if A - B = the empty set.

    I'm a little lost at how to do this... could someone point me in the right direction?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MacstersUndead's Avatar
    Joined
    Jan 2009
    Posts
    291
    Thanks
    32
    Suppose not. Suppose that A is a subset of B and A - B =! the empty set.

    That is, WLOG, that A - B = {x_i}, some element in A.

    Then A = B + {x_i}, but this contradicts the definition of a subset.

    (I think this is sufficient, not entirely sure, but I think it follows intuition nicely)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    66
    That makes sense. Thanks for your help!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Proof that if A is a subset of P(A), P(A) is a subset of P(P(A))
    Posted in the Discrete Math Forum
    Replies: 12
    Last Post: May 23rd 2011, 04:26 PM
  2. subset
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 4th 2011, 01:14 PM
  3. Proof on Openness of a Subset and a Function of This Subset
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: October 24th 2010, 09:04 PM
  4. subset U subset is NOT subspace of Superset?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 20th 2009, 04:17 PM
  5. Subset tst
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 11th 2007, 09:28 AM

Search Tags


/mathhelpforum @mathhelpforum