Results 1 to 5 of 5

Thread: Is this set theory statement true?

  1. #1
    Newbie
    Joined
    Nov 2011
    Posts
    12

    Question Is this set theory statement true?

    I think it is, but if someone could explain why or why not, it would be greatly appreciated.

    {4} ∈ P{6,4,3,2,5}

    Many thanks! I'm just getting my head around set theory.
    (The P is a power set symbol by the way!)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,577
    Thanks
    790

    Re: Is this set theory statement true?

    $\displaystyle A\in P(B)$ means the same thing as $\displaystyle A\subseteq B$. Here, it is clearly true that $\displaystyle \{4\}\subseteq\{6,4,3,2,5\}$.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2011
    Posts
    12

    Re: Is this set theory statement true?

    Your help is much appreciated, thank you. I never realised that it meant the same thing.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Aug 2011
    Posts
    128

    Re: Is this set theory statement true?

    Quote Originally Posted by emakarov View Post
    $\displaystyle A\in P(B)$ means the same thing as $\displaystyle A\subseteq B$.
    This is almost always true, but not quite. You can apply $\displaystyle A\subseteq B$ in some cases when B is a proper class (and even if A is a proper class), but you can't take the power set of a proper class so $\displaystyle A\in P(B)$ is not a valid statement. For example, it makes sense to say that the class of all ordinals form a subset of the class of all sets, and I can describe this in first-order logic without getting into paradoxes. However, it doesn't make sense to refer to the power set of the class of all sets (such a set does not exist).

    The important idea here is that the power set of a set X, is the collection of all X's subsets. So the members of P(X), when P(X) is a set, are precisely those things that are subsets of X.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2011
    Posts
    15

    Re: Is this set theory statement true?

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Where is this statement true?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Oct 21st 2011, 11:42 AM
  2. [SOLVED] Is the converse statement true?
    Posted in the Number Theory Forum
    Replies: 9
    Last Post: Jun 3rd 2010, 05:23 AM
  3. True or False Statement?
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: Feb 11th 2009, 08:04 AM
  4. [SOLVED] Is this statement true?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: Jan 28th 2009, 01:18 AM
  5. true statement
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: Jul 27th 2006, 11:16 PM

Search Tags


/mathhelpforum @mathhelpforum