# 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?

1
by sayandeb

2014-08-27T13:18:41+05:30

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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

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