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

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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?
 
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