Question

Let A and B be subsets of a universal set U and suppose n(U)=400, n(A)=135, n(B)=80, and n(A n B)=60. Find the number of elements in the set n(Ac n Bc)

Answer 1

use A' for A complement, etc. and n = intersection ∩.
n(A' n B')
=n(A u B)' by the de Morgan's law
=nU-n(nA+nB-n(AnB)) n(A u B) = nA + nB - n(AnB) and nX'=nU-nX
=400-(135+80-60)
=400-155
=245