Question 429443
(a) n(A ∩ (B U C)) =  n((A ∩B) U (A ∩C))

= n(A ∩B) + n(A ∩C) - n(A ∩ B ∩ C)

= 8 + 9 - 5 = 12.

(b)  {{{B U C}}} and {{{(B U C)^c}}} are disjoint, hence  so are A ∩ {{{B U C}}} and A ∩ {{{(B U C)^c}}}.
==> nA = n(A ∩ {{{B U C}}} ) + n(A ∩ {{{(B U C)^c}}})
==> 23 = 12 + n(A ∩ {{{(B U C)^c}}})
==> n(A ∩ {{{(B U C)^c}}}) = 11.