Answer to Question #203117 in Discrete Mathematics for roni

Question

There were 100 students in the library who responded to how they completed their research papers.

• 18 students only used the periodicals.

• 29 students used the web and books.

• 15 students used books, the web, and periodicals.

• 40 students used books and periodicals.

• 20 used the web and periodicals.

• 60 students used books.

• 7 students did not use the web, nor books, nor periodicals.

a) Represent this information with a Venn diagram.

b) How many students only used the web in their research?

c) How many students used books or periodicals?

Answer 1

Given

total student=100

students used only periodicals=18

students used web and books.=29

students used books,web, and periodicals=15

students used books and periodicals=40

students used web and periodicals=20

students used books=60

students did not use the web, nor books, nor periodicals=7

now

students used books,web, and periodicals=15

students used only web and periodicals=20-15

students used only web and books=29-15=14

students used only books and periodicals=40-15=25

students used only books=60-25-15-14=6

students used only web=100-60-18-5=10

students used only periodicals=18

(a)Venn diagram

(b) How many students only used the web in their research?

students used only web=93-60-18-5

=10

(c) How many students used books or periodicals?

students used books or periodicals=(students used books) +(students used periodicals)-(students used books and periodicals)

=60+63-40

=83

other method

students used books or periodicals=total student - students used only web - students did not use the web, nor books, nor periodicals

=100-10-7

=83