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!

Intro Real Analysis ?

  1. Sep 15, 2007 #1
    Let f: X--> Y where X and Y are arbitrary sets. Show the following are equivalent.

    a. F is 1-1 on X
    b. f(A/B)=f(A)/f(B) for all subsets A and B of X
    c. f^-1 f(E) = E for all E that is a subset of X
    d. f(A intersect B) = f(A) union f(B) for all A,B that is a subset of X

    I know that in order to f to be 1-1 on X one value of x corresponds to one value of Y. For example f(x1)=a and x1 does not equal x2 so therefore f(x2) can't equal a. Other than that I don't know where to start to show that these all imply the other. I am also having a hard time understanding what b and d even mean. Any help would be great.
  2. jcsd
  3. Sep 15, 2007 #2
    Try to write out in words what these means.
    For example f(A/B) = { f(x) | x in A but x not in B}.
    This makes it much easier.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Intro Real Analysis Date
Intro to real analysis Apr 17, 2014
Intro To real analysis problem Apr 23, 2012
Intro to Real Analysis: Supremum Sep 18, 2011
Intro to Real Analysis Sep 15, 2011
A simple Intro to Real Analysis question Oct 1, 2010