- #1

- 584

- 0

## Homework Statement

Let g be a function from ℝ to ℝ and for all subsets A and B of R.

## Homework Equations

Prove that:

[tex]g^{-1}(A\cup B)=g^{-1}(A)\cap g^{-1}(B)[/tex]

and

[tex]g^{-1}(A\cap B)=g^{-1}(A)\cup g^{-1}(B)[/tex]

## The Attempt at a Solution

Our teacher gave us this problem but I think it's wrong because I was easily able to prove that:

[tex]g^{-1}(A\cup B)=g^{-1}(A)\cup g^{-1}(B)[/tex]

and

[tex]g^{-1}(A\cap B)=g^{-1}(A)\cap g^{-1}(B)[/tex]

but when i try to solve what he gave us this is all I can do:

[tex]x\in g^{-1}(A\cup B)\Longleftrightarrow g(x)\in A\cup B\Longleftrightarrow g(x)\in Aorg(x)\in B\Longleftrightarrow x\in g^{-1}(A)\cup g^{-1}(B)[/tex]

and the same goes for the second one. Can anyone tell me where I'm going wrong?