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: Union and Intersections proofs for real analysis

  1. Sep 12, 2009 #1
    Hi,

    I have four similar problems that I am not sure how to do: Given: A1 and A2 are in X, B1 and B2 are in Y f: X->Y, g - inverse of f
    I have to either prove or if false find counterargument
    1. f(A1 U A2) = f(A1) U f(A2)
    2. f(A1 n A2) = f(A1) n f(A2)
    3. g(-1)(B1 U B2) = g(B1) U g(B2)
    4. g(B1 n B2) = g(B1) n f(B2)

    I started doing 2. I was able to show that f(A1 n A2) C=(is contained in) f(A1) n f(A2):
    let x € f(A1) and x € f(A2)
    since (A1 n A2) <=A1, x€f(A1)
    since (A1 n A2) <=A2, x€f(A2)
    => x € f(A1 n A2), x € f(A1) n f(A2), i.e. (A1 n A2) C= f(A1) n f(A2)

    But I am not sure how to show the other way, i.e. that f(A1) n f(A2) C= (A1 n A2), in order to conclude that both expressions are equal. Or are they equal at all?
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Loading...