Question

25 item
5.
a) find n(a and b)
set n(only a)= 11
set .only b)= 8

practice questions
#1) in class of 30 student
18 students take math
12 student take science
7 student take math and science
a)3 students b) 9 student c) 12

#2) a survey asked students which sports they play. there are 20 student
6 play both soccer and basketball
15 play soccer
11 play basketball
a)

#3) let the universal set u be the numbers from 1 to 20.
set a = multiples of 3/ u{3,6,9,12,15,18} >a
set b = multiples of 5/ u{5,10,15,20}
b) set a=5 b=3
c)3 n(u)=6 n(a)=3 n(a)=3

Explanation:

Step1: Solve #1 (Only Math)

$n(\text{only Math}) = n(\text{Math}) - n(\text{Math and Science}) = 18 - 7 = 9$

Step2: Solve #2 (Fill Venn Diagram)

Step2a: Only Soccer

$n(\text{only Soccer}) = n(\text{Soccer}) - n(\text{both}) = 15 - 6 = 9$

Step2b: Only Basketball

$n(\text{only Basketball}) = n(\text{Basketball}) - n(\text{both}) = 11 - 6 = 5$

Step2c: Neither sport

$n(\text{neither}) = n(U) - [n(\text{only Soccer}) + n(\text{only Basketball}) + n(\text{both})] = 20 - (9+5+6) = 0$

Step3: Solve #3 (Set Operations)

Step3a: List sets

$A = \{3,6,9,12,15,18\}$, $B = \{5,10,15,20\}$, $U = \{1,2,...,20\}$

Step3b: $n(A)$, $n(B)$

$n(A)=6$, $n(B)=4$

Step3c: $n(A \cap B)$

$A \cap B = \{15\}$, so $n(A \cap B)=1$

Step3d: $n(A')$

$n(A') = n(U) - n(A) = 20 - 6 = 14$

Answer:

#1: b) 9 students
#2: Venn Diagram: Only Soccer = 9, Both = 6, Only Basketball = 5, Neither = 0
#3:
a) $A=\{3,6,9,12,15,18\}$, $B=\{5,10,15,20\}$
b) $n(A)=6$, $n(B)=4$
c) $n(A \cap B)=1$, $n(A')=14$