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)

Question

Gustavo Wiggins

Mathematics

30 July, 04:49

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)

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Answers (1)

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Maleah Chen · 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