Thread: subsets problem in metric spaces

let X be a metric space and A an open subset of X
Prove that A ∩ B⁻ ⊂ (A∩B)⁻

My approach:
let x∈A ∩ B⁻
Then x∈A and x∈B⁻
nbhd(x) intersects A and B for all ε >0
so x∈ A⁻∩ B⁻
but (A∩B)⁻ ⊂A⁻∩ B⁻
Did I do anything wrong or miss something?

**I was Wrong