Results 1 to 4 of 4

Thread: Problems with sets

  1. #1
    Newbie
    Joined
    Mar 2017
    From
    San Marino
    Posts
    18

    Problems with sets

    Hi, does someone know the solution to the problem:
    Problems with sets-untitled.png

    So sorry if it has nothing to do with sets, I just have no idea what this is in English.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Mar 2017
    From
    San Marino
    Posts
    18

    Re: Problems with sets

    And another one, that has definitely to do with sets:

    if A ⊆ B, prove that A ∪ B = B, and A ∩ B = A.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    19,416
    Thanks
    2889

    Re: Problems with sets

    Have you calculated the first few A_i? The first problem only requires the first four and you should be able to see what others are like.
    With i= 1, A_i is the set of all x such that 1- \frac{1}{1}< x\le 1 which is the same as 0< x \le 1. In interval notation that is (0, 1].
    With i= 2, A_2 is the set of all x so that 1- \frac{1}{2}< x\le 2. In interval notation, that is (1/2, 2].

    With i= 3, A_3 is the set of all x such that 1- \frac{1}{3}< x\le 3. In interval notation, that is (2/3, 3].

    With i= 4, A_4 is the set of all x such that 1- \frac{1}{4}< x\le 4. In interval notation, that is (3/4, 4].

    The union of those is the interval (0, 4].

    For the last, to prove that two sets, X and Y, are equal, first prove X\subset Y, then prove Y\subset X. And to prove that X\subset Y, start "if x\in X and use the definitions and properties to conclude "therefore x\in Y".

    For example, given that A\subset B, to show that A\cup B= B:
    First show [b]B\subset A\cup B[/tex]. That's easy. If x\in B then, by definition of "union", x\in A\cup B.

    Now show [b]A\cup B\subset B[/tex]. If x\in A\cup B then either (1) x\in A or (2) x]in B.

    1) if x\in A then since we are given that A\subset B, x\in B.
    2) if x\in B, we are done.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Mar 2017
    From
    San Marino
    Posts
    18

    Re: Problems with sets

    That makes a lot of sense, thank you so much! I've yet to have a course in discrete math, but ran across these problems so I had no idea where to begin, but was very curious to see the solution. Now I see how obvious it was. Thanks again!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Metric spaces, open sets, and closed sets
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: Mar 16th 2011, 06:17 PM
  2. Replies: 9
    Last Post: Nov 6th 2010, 01:47 PM
  3. problems about finding bargaining sets
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: Apr 19th 2009, 05:45 AM
  4. Replies: 3
    Last Post: Jul 10th 2007, 02:40 PM
  5. sets and set notation 3 problems
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Dec 3rd 2006, 12:19 PM

/mathhelpforum @mathhelpforum