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!

Power sets

  1. Oct 14, 2009 #1
    1. The problem statement, all variables and given/known data

    Prove [tex]P(A) \cup P(B) \subseteq P(A \cup B) [/tex]

    2. Relevant equations

    3. The attempt at a solution

    I started out by assuming that [tex] A = \left\{a\right\} [/tex] and [tex]B=\left\{b\right\}[/tex].

    So then [tex]P(A) \cup P(B) = \left\{\left\{a\right\},\left\{b\right\},null\right\}[/tex] and [tex]P(A \cup B) = \left\{\left\{a\right\},\left\{b\right\},\left\{a,b\right\},null\right\}[/tex]

    So I can conclude that [tex]P(A) \cup P(B) \subseteq P(A \cup B) [/tex]

    How does that sound?
  2. jcsd
  3. Oct 14, 2009 #2
    When you assume that A={a} and B={b}, you are assuming that A and B are both singleton sets. You want to prove the relation for any sets A and B.

    When proving one set is a subset of another, say X is a subset of Y, then you let x be in X and show x is in Y. So let [itex]x\in P(A)\cup P(B)[/itex], and then show [itex]x\in P(A\cup B)[/itex].
  4. Oct 14, 2009 #3
    Okay, so let [tex]x\in P(A)\cup P(B)[/tex].
    Then [tex]x\in P(A)[/tex] or [tex]x\in P(B)[/tex]... which means [tex]x\subseteq A[/tex] or [tex]x\subseteq B[/tex]?

    So then [tex]x\subseteq (A\cup B)[/tex]. Am I going in the right direction?
  5. Oct 14, 2009 #4


    User Avatar
    Science Advisor

    Very good, the conclusion now follows.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Power sets
  1. Power Sets (Replies: 4)

  2. The Power Set (Replies: 1)

  3. Power set (Replies: 2)

  4. Power set? (Replies: 4)