# Venn Diagrams

A recent survey of a group of students found that many participate in baseball, football and soccer. The Venn diagram below shows the results of the survey.

a) How many students participated in the survey?

b) How many of these students play both soccer and baseball?

c) How many play only 1 sport?

Given A = {a, b, c, d, e}

B = { a, b, d, f, g}

C = {b, c, e, g, h}

D = {d, e, f, g, h}

Find:

a) A B

b) (A D) B

c) A (B D)2

https://brainmass.com/math/discrete-math/set-theory-venn-diagrams-345232

#### Solution Preview

A recent survey of a group of students found that many participate in baseball, football and soccer. The Venn diagram below shows the results of the survey.

a) How many students participated in the survey?

Add all numbers in the diagram. We'll have 21 students. Each of them played at least one sport, since there's no numbers outside of the circles.

b) How many of these students play both soccer and baseball?

We need the overlap of the ...

#### Solution Summary

Venn Diagrams are examined.