Question

A travel agency surveyed 1000 people to find out how many of them visited London and Paris. 310 people vistied London, 222 people visited Paris and 118 people visited both cities. How many people vistied none of these cities? A.414 B.104 C.192 D.586

Answer 1

586

Explanation:

Using set notation to answer the question.

let n(U) be the total number of people surveyed = 1000

n(L) be number of people that visited London = 310

n(P) be number of people that visited Paris = 222

n(P∩L) be number of people that visited both cities = 118

n(P∪L)' be number of people that visited none of the cities = x

n(U) = n(PUL) + n(PUL)'

We willl get n(PUL) using the formula;

n(PUL) = n(P)+ n(L)-n(P∩L)

n(PUL)= 222+310-118

n(PUL)= 414

Since n(U) = n(PUL) + n(PUL)'

1000 = 414+n(PUL)'

n(PUL)' = 1000-414

n(PUL)' = 586

586 peoples visitied none of these cities?