Let (X,D)be a metric space and let A and B be subset of X.Define D(A,B)=in f⁡{D(

Let (X,D)be a metric space and let A and B be subset of X.Define D(A,B)=in f⁡{D(a,b):a∈A,b∈B}
Prove that if some sequence of points in A converges to a point in B,then D(A,B)=0.that if some sequence of points in A converges to a point in B,then D(A,B)=0.
Hint: Proof by contradiction