(a) Give a recursive definition for the intersection of the sets A1, A2, . . . , An, An+1 ⊂ °U, n > 1.
(b) Use the result in part (a) to show that for all n, r ∈ Z+ with n > 3 and 1 < r < n,
(A1 ∩ A2 ∩ ∙ ∙ ∙ ∩ Ar) ∩ (Ar+1 ∩ ∙ ∙ ∙ ∩ An) = A1 ∩ A2 ∩ ∙ ∙ ∙ ∩ Ar ∩ Ar+1 ∩ ∙ ∙ ∙ ∩ An.