1. Not finding help here? Sign up for a free 30min 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!

Inquiry about proofs involving families of sets

  1. Jan 11, 2012 #1
    1. The problem statement, all variables and given/known data

    This post does not concern a particular problem or exercise, but instead a peculiarity (for me) in one genre: proofs involving families of sets (that is, sets containing sets as elements). I have noticed that in some statements of theorems which involve families of sets, the hypothesis includes " let F and G be families of sets," whereas in others, the hypothesis is slightly altered to: "let F and G be nonempty families of sets." I have included two theorems (which I have already proven) as examples of this:

    1. Suppose F and G are nonempty families of sets. Prove that U(F U G) = (UF) U (UG).

    2. Suppose F and G are families of sets. Prove that U(F ∩ G) ⊆ (UF) ∩ (UG).


    2. Relevant equations



    3. The attempt at a solution

    The difference obviously regards some property about the empty set. My original thought was that being nonempty allowed for the assertion of F or G containing some set- which arises during the course of the proof of 1. That is, x ∈ U(F U G) means there is some A ∈ F U G for which x ∈ A. But then, however, i noticed that the proof of theorem 2. also asserts the existence of some set which is an element of F (and G), without the "nonempty" portion of the hypothesis being present. Could this simply be a mistake on the part of the author, or am i missing a notion here?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Inquiry about proofs involving families of sets
  1. Fine Families Proof (Replies: 0)

Loading...