80 investors were surveyed. All investors had either 1 mutual fund or 2 stocks.50 had 1 mutual fund, and 55 had 2 stocks . How many investors had 1...

We represent the entire set of investors
as I.

Let M be the set mutual fund investors. Let S be the set of
ivstors in stocks.

Then I  = MUS

The
number of investors = n(I) = 80.

the number of investors in mutual
fund = n(M) = 50.

The number of investors in stocks = n (S) =
55.

Therefore, I = M U S

n(NUS) = n(M)
+n(m) - n(N & S).....................(1), where (N&S)  represents  set of
investors investing in both N  and S

Therefore , from(1) , we get:
n(N&S) =  n(M) + n(S) - n(M U S).

Given that n(MUM) = 80 ,
n(M ) = 50 , n(S) = 55,

Therefore n(M &S) = 50+55-80 =
105-80 = 25.

Therefore there are 25 investors who invested in both
mutual fund and stocks.