Please provide steps for proof.

3. (3 points total) Post-Processing and Independence (3 points) Suppose X and Y are Bernoulli random variables, and /: (0,1) -> (0, 1) is a function. Prove that if X and Y are independent then f(X ) and Y are independent. Note: In fact, this works for any random variables, not just Bernoulli once, and any function from R to R. Optional Challenge Exercise