Simple measure theory questions (inverse image)

[EV33]

Homework Statement

I was wondering if we Let E be some set such that f^-1(E) is measurable then so is f^-1(E)^c.

Homework Equations

If the set A is measurable then so is its compliment.

The Attempt at a Solution

I think the statement is true because f^-1(E) is just a set and thus its compliment should also be measurable.Thank you for your time.

 

[micromass]

Yeah that is correct.