Topological Proof: Showing bdy(A) ∩ bdy(B) C bdy(A ∩ B)

[tracedinair]

Homework Statement

Let boundary = bdy, ∩ = intersection and C = contained. Show that the bdy (A) ∩ bdy(B) C bdy (A ∩ B).

Homework Equations

The Attempt at a Solution

I can draw a diagram of this idea and visualize it my mind, but I cannot formally show this (this is second proof I've attempted). Can anyone help me get it started?

 

[Mark44]

And what are A and B?