Question

A group of 40 americans came to visit Kolkata, 25 visited Victoria  Memorial, 15 visited Indian Museum and 7 did not visit either of the two. Draw a venn diagram and find the following.
a) How many visited both the places?
b) How many visited only Indian museum?

Answer 1

N = 40
A = set of those who visited Victoria Memorial
B = set of those who visited Indian Museum

Set of those who visited both places = A Intersection B

Number of Americans visiting Victoria M or Indian M = M(A U B)  = m(U) - (A U B)'
        =>   m(A U B) = 40 - 7 = 33
        =>   m (A) + m(B) - m (A intersection B) = 33
        =>    25 + 15 - m(A intersection B) = 33

So,   m (A intersection B) = 7  = number of Americans who visited BOTH.

Number of Americans who visited ONLY Indian Museum =
                   m (B \ A) = m(B - A) = m(B) - m(B intersection A)
                                 = 15 - 7 = 8