Patrons of a local bookstore can sign up for advance notification of new book ar
ID: 3644166 • Letter: P
Question
Patrons of a local bookstore can sign up for advance notification of new book arrivals in genres of interest. In the first month of this service, 32 sign up for mysteries, 34 for spy novels, 18 for westerns, and 41 for science fiction. Of these, 17 sign up for both mysteries and spy novels, 8 for both mysteries and western, 18 for mysteries and science fiction, 5 for spy novels and westerns, 20 for spy novels and science fiction, and 12 for western and science fiction. In addition, 2 sign up for mysteries, spy novels, and westerns; 11 for mysteries, spy novels, and science fiction; 6 for mysteries, westerns, and science fiction; and 5 for spy novels, westerns, and science fiction. Finally, 2 people sign up for all four categories. How many people signed up for service in the first month? (Note: show the formula of principle of inclusion and exclusion extended to four sets and then provide solution.)Explanation / Answer
M = Signed up for mystries S = signed up for spy W = signed up for westerners F = signed up for science fiction To find : |M U S U W U F| Formula: |M U S U W U F| = |M|+|S|+|W|+|F| - |M.S| - |M.W|- |M.F|- |S.W|- |S.F|- |W.F|+|M.S.W|+|M.W.F|+|M.S.F|+|S.W.F|-|M.S.W.F| {A.B= A intersection B} =32+34+18+41-17-8-18-5-20-12+2+6+11+5-2 = 67 Hence the answer is 67