Answer to Question #203028 in Discrete Mathematics for lucy

Question

There were 100 students in the library who responded to how they completed their research paper. • 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 the periodicals. a) Represent this information with a Venn diagram. (8 marks) b) How many students only used the web in their research? (2 marks) c) How many students used books or periodicals?

Answer 1

a)

$N(P\cap B'\cap W')=18$

$N(B\cap W)=29$

$N(B\cap W\cap P)=15$

$N(B\cap W\cap P')=N(B\cap W)-N(B\cap W\cap P)$

$=29-15=14$

$N(B\cap P)=40$

$N(B\cap P\cap W')=N(B\cap P)-N(B\cap P\cap W)$

$=40-15=25$

$N(W\cap P)=20$

$N(W\cap P\cap B')=N(W\cap P)-N(B\cap P\cap W)$

$20-15=5$

$N(B)=60$

$N(B\cap P'\cap W')=N(B)-N(B\cap W)-N(B\cap P)$

$+N(B\cap W\cap P)=60-29-40+15=6$

$N(B'\cap W' \cap P')=7$

$N(W\cap B'\cap P')=100-N(B'\cap W' \cap P')$

$-N(P\cap B'\cap W')-N(W\cap P\cap B')$

$=100-7-60-18-5=10$

b)

$N(W\cap B'\cap P')=10$

c)

$N(B\cup P)=N(B\cap W'\cap P')+N(P\cap B'\cap W')$

$+N(B\cap P)=6+18+40=64$