1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Discrete Math - question about sets

  1. Nov 2, 2009 #1
    1. The problem statement, all variables and given/known data

    Use set builder notation to give a description of each of these sets.

    a) { 0,3,6,9,12 }

    b) { -3, -2, -1,0, 1, 2, 3 }

    c) { m,n,o,p }

    3. The attempt at a solution

    X={x l x is an odd possitive multiplier of 3 less than 12 }

    X is supposed to be the set. Can I just name it randomly? Also, can I say it like this? Is that ok? Not really sure about b and c.
  2. jcsd
  3. Nov 2, 2009 #2
    You can name your set what you like.

    For b, notice the elements are integers from -3 to 3; that is, x[tex]\in[/tex]Z AND -3 [tex]\leq[/tex] x [tex]\leq[/tex] 3

    For a, x does not have to be odd since 6 and 12 are in the set. You are right that they are positive multiples of 3 and less than 12 but can you describe that in mathematical notation?
  4. Nov 2, 2009 #3

    Oh yeah.. nevermind. They are not all odd.

    And no, I don't know. I'd just simply say : X= { x[tex]\in[/tex]Z l x is positive x*3 less than 13 }
  5. Nov 2, 2009 #4
    If you denote 3Z as the set multiples of three, then the set in (a) consists of elements x [tex]\in[/tex]3Z such that 0 [tex]\leq[/tex] x [tex]\leq[/tex] 12
  6. Nov 2, 2009 #5
    Alternatively, if you've seen quantifiers before you can write the set as

    [tex] \left\{0,3,6,9,12\right\} = \left\{ x \in \mathbb{Z} \mid \exists y \in \mathbb{Z} \left(x=3y\right), 0 \leq x \leq 12 \right\}[/tex].

    The first predicate essentially says that x is included in the set if and only if there exists an integer y such that x is three times y.

    For example, the number 4 would not be included in the set because there is no integer that satisfies [tex]4=3y[/tex]. If you haven't seen quantifiers yet, then nevermind. :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook