Survey Diagram for a Mathematical Venn Question
A survey was conducted among 76 patients admitted to a hospital cardiac unit during a​ two-week period. The data of the survey are shown below.

Let B = the set of patients with high blood pressure.
Let C = the set of patients with high cholesterol levels.
Let S = the set of patients who smoke cigarettes.

Use the conditions given above to answer the following questions.
a. Find the number of these patients that had either high blood pressure or high cholesterol​ levels, but not both.
b. Find the number of these patients that had fewer than two of the indications listed.
c. Find the number of these patients that were smokers but had neither high blood pressure nor high cholesterol levels.
d. Find the number of these patients that did not have exactly two of the indications listed.

A middle school​ counselor, attempting to correlate school performance with leisure​ interests, found that of a group of​ students, 32 had seen Movie​ A, 27
had seen Movie​ B, 24 had seen Movie​ C, 15 had seen Movies A and​ B, 11 had seen Movies A and​ C, 8 had seen Movies B and​ C, 3 had seen all three​ films, and 6
had seen none of the three films. Use a Venn diagram to complete parts​ (a) through​ (c) below.

Complete a Venn diagram considering the following classifications.
Complete the Venn diagram. Let A be the set of students that saw Movie​ A, B be the set of students that saw Movie​ B, and C be the set of students that saw Movie C.

Also, answer the following questions about the Venn Diagram
a) How many students had seen Movie C​ only?
b) How many students had seen exactly two of the​ films?
c) How many students were​ surveyed?
The following Venn Diagram is a graphical representation of the relationship between the conditions, and can help you in answering the questions.

Solved Venn Diagram for the Math Reasoning question

An example of a Math question from a Math reasoning class. The problem is from a Venn's diagram lesson.
The 65 students in a classical music lecture class were​ polled, with the results that 36 like Wolfgang Amadeus​ Mozart, 37 like Ludwig von​ Beethoven, 33 like Franz Joseph​ Haydn, 14 like Mozart and​ Beethoven, 21 like Mozart and​ Haydn, 15 like Beethoven and​ Haydn, and 8 like all three composers. Use a Venn diagram to complete parts​ (a) through​ (f) below.

a) How many of these students like exactly two of these​ composers?
b) How many of these students like exactly one of these​ composers?
c) How many of these students like none of these​ composers?
d) How many of these students like​ Mozart, but neither Beethoven nor​ Haydn?
e) How many of these students like Haydn and exactly one of the other​ two?
f) How many of these students like no more than two of these​ composers?

A bass guitarist worked on 9 music projects last year. He wrote and produced 3
projects. He wrote a total of 5 projects. He produced a total of 7 projects. Use a Venn diagram to determine​ (a) how many projects he wrote but did not​ produce, and​ (b) how many projects he produced but did not write.

Question: Complete the Venn diagram. Let W be the set of projects the bass guitarist wrote and P be the set of projects he produced.
View Image for the Venn Diagram.