a) If A and B be two subsets of universal set U such that n(U) = 350 , n(A) = 100 , n(B) = 150 , and n(A B) = 50 , then find n( A B) . b) If a, b, c are in A.P., b, c, d are in G.P., and c, d, e are…

a) If $A$ and $B$ be two subsets of universal set $U$ such that $n(U)=350$, $n(A)=100$, $n(B)=150$, and $n(A\cap B)=50$, then find $n(\overline{A}\cap \overline{B})$. b) If $a,b,c$ are in A.P., $b,c,d$ are in G.P., and $c,d,e$ are in H.P., then prove that $a,c,e$ are in G.P.