SOLUTION: Resorts. In a survey of 65 resorts, it was found that 34 provided refrigerators in the guest rooms 30 provided laundry services 37 provided child care services 15 provided refr

In this problem, you are given a universal set of 65 resorts,
and 3 (three) its subsets

    R = {provided refrigerators in the guest rooms};  n(R) = 34;

    L = {provided laundry services};                  n(L) = 30;

    C = {provided child care services};               n(C) = 37.


You are also given the number of elements in each in-pair intersetion

    n(RL) = 15;  n(RC) = 17;  n(LC) = 19,

and in the triple intersection n(RLC) = 7.


        +-----------------------------------------------+
        |    Now I answer questions, one after other.   |
        +-----------------------------------------------+


(a)  n(R_only) = n(R) - n(RL) - n(RC) + n(RLC) = 34 - 15 - 17 + 7 = 9.



(b)  To answer (b), calculate n(L_only) and n(C_only similarly.

     Then compute n(R_only) + n(L_only) + n(C_only).

     I leave it to you, since after my instructions, it is just simple arithmetic.



(c)  Use the inclusion-exlusion principle formula for the union (R U L U C)

         n(R U L U C) = n(R) + n(L) + n(C) - n(RL) - n(RC) - n(LC) + n(RLC) = 

                      = 34   + 30   + 37   -  15   -  17   -  19   +   7 = 57.



(e)  is the complement of n(R U L U C) to 65, so the answer to (e) is 65 - 57 = 8.



(d)  To answer (d), you should calculate n(RL_only), n(RC_only) and n(LC_only).

     Each of these three numbers is calculated following the same scheme.  

     For example, n(RL_only) = n(RL) - n(RLC) = 15-7 = 8.


     So, calculate n(RC_only) and n(LC_only) similarly;

     then compute the sum  n(RL_only) + n(RC_only) + n(LC_only).