Question

In a survey, 500 people were asked if they had ever visited Paris, London or Vienna. The compilation of responses will indicate:22 people visited the three capitals50 people visited Paris and London18 people visited London and Vienna only75 people visited Paris only94 People have visited London7 People visited Vienna Only312 people did not visit any of the three citiesA) What is the Universal set UB) Represent this situation by a Venn diagram indicating the number of elements in each section of the diagram.C) All the people who visited Paris and ViennesD) All the people who visited Paris and Viennes and not London.

Answer 1

Step 1

What is the Universal set U

The universal set is a set that contains all elements including itself.

For this question, the universal set U is

`U=\text{ 500}`

Step 2

Represent this situation by a Venn diagram

Step 3

All the people who visited Paris and Vienna

`\begin{gathered} x\text{ represents the number of people who visited Paris and Vienna only} \\ 75+28+26+22+18+x+7+312=500 \\ 488+x=500 \\ x=\text{ 500-488} \\ x=\text{ 12} \end{gathered}`

Hence, all the people who visited Paris and Vienna is given as

`12+22=\text{ 34}`

Step 4

All the people who visited Paris and Vienna and not London

`\begin{gathered} =34\text{ - 22} \\ =\text{ 12} \end{gathered}`