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 sell yam and plantain only while 3 sell all the three items. How many women are in the group?

Let P = {1, 2, u, v, w, x}; Q = {2, 3, u, v, w, 5, 6, y} and R = {2, 3, 4, v, x, y}.

Determine (P-Q) ∩ R

In a youth club with 94 members, 60 like modern music, and 50 like traditional music. The number of members who like both traditional and modern music is three times those who do not like any type of music. How many members like only one type of music?

If U = {x : x is an integer and 1 \(\leq\) x \(\leq\) 20}
E\(_1\) = {x : x is a multiple of 3}
E\(_2\) = {x : x is a multiple of 4}
and an integer is picked at random from U, find the probability that it is not in E\(_2\)

If X = {n\(^2\) + 1:n = 0,2,3} and Y = {n+1:n=2,3,5}, find X∩Y.