Let f: X--> Y where X and Y are arbitrary sets. Show the following are equivalent.(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Intro Real Analysis ?

**Physics Forums | Science Articles, Homework Help, Discussion**