SOLUTION: A group of market women sell at least one of yam, plantain and maize. 12 of them sell maize, 10 sell yam and 14 sell plantain. 5 sell plantain and maize, 4 sell yam and maize, 2 se

We are given a set of women, which consists of 3 intersecting subsets, 

    - Y (sell yam and may be something else),
    - P (sell plantain and may be something else),
    - M (sell maize and may be something else).


About these sets and their intersections, we are given the following information

    n(M) = 12,                                                 (1)
    n(Y) = 10,                                                 (2)
    n(P) = 14,                                                 (3)

    n(PM) = 5       (for intersection P and M)                 (4)
    n(YM) = 4       (for intersection Y and M)                 (5)
    n(YP\YMP) = 2   ((for intersection Y and P) minus YMP)     (6)

    n(MYP) = 3      (for triple intersection Y, M and P).      (7)


Now, from (6) and (7), we get  

    n(YP) = n(YP\YMP) + n(YMP) = 2 + 3 = 5.                    (8)


    +-------------------------------------------+
    |    They want we determine n(M U Y U P).   |
    +-------------------------------------------+


Use the Inclusive-Exclusive principle formula

    n(M U Y U P) = n(M) + N(Y) + n(P) - n(PM) - n(YM) - n(YP) + n(YMP).


Substitute here all known quantities and get the answer

    n(M U Y U P) = 12 + 10 + 14 - 5 - 4 - 5 + 3 = 25.


ANSWER.  There are 25 women in the group.