问题11。在对60人的调查中，发现25人阅读报纸H，26人阅读报纸T，26人阅读报纸I，9人阅读H和i，11人同时阅读H和T，I，3人阅读全部三份报纸。找：
(i)至少阅读过该报纸之一的人数：
(ii)准确阅读一份报纸的人数。
解决方案：
(i) Let n(P) denote the total number of people.
n(H) denote the total number who read newspaper H
n(T) denote the total number who read newspaper T
n(I) denote number of people who read newspaper I
According to formula:
n(P)=60, n(H)= 25, n(T)=26, n(I)=26
n(H∩I)= 9, n(H∩T)=11, n(T∩I)=8, n(H∩T∩I)=3
Here we need to find, number of people who read at least one of the newspaper:
i.e. (H∪T∪I)
n(H∪T∪I) = n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) – n(A∩C) + n(H∩T∩I)
= 25+26+26-9-11-8+3
=25+52-28+3
=52
(ii) The number of people who read newspaper H only = 25 – (8+3+6) = 8
The number of people who read newspaper T only = 26 – (8+3+5) = 10
The number of people who read newspaper I only = 26 – (6+3+5) = 12
The number of people who read exactly one newspaper = 8+10+12 =30
问题12.在某所学校的三支运动队的成员中，篮球队有21名，曲棍球队有26名，足球队有29名。 14人打曲棍球和篮球，15人打曲棍球和足球，12人打橄榄球和篮球，8人打全部三场比赛。总共有几位成员?
解决方案：
Let assume that
n(P) is the number of members in the basketball team.
n(B) is the number of the people in the basketball team.
n(H) is the number of the people in the hockey team.
n(F) is the number of the people in the Football team.
n(B) = 21 n(H) = 26 n(F) = 29
n(H ∩ B) = 14 n(H ∩ F) = 15 n(F ∩ B) = 12, n(H ∩ B ∩ F) = 8
P = B ∪ H ∪ F
n(P) = n(B ∪ H ∪ F)
= n(B) + n(H) + n(F) – n(B ∩ H) – n(H ∩ F) – n(B ∩ F) + n(B ∩ H ∩ F)
21 + 26 + 29 – 14 – 15 – 12 + 8 = 43
问题13.在1000人的小组中，有750个会说北印度语的人和400个会说孟加拉语的人。有多少人只会讲北印度语/有多少人会说孟加拉语?印地语和孟加拉语有多少人会说?
解决方案：
Let assume that
n(P) the number of people
n(H) the number of people who can speak Hindi
n(B) the number of people who can speak Bengali
n(P) = 1000 n(H) = 750 n(B) = 400
P = (H ∪ B) = n(H) + n(B) – n(H ∩ B)
1000 = 750 + 400 – n(H ∩ B)
n(H ∩ B) = 150
So we can say that 150 can speak both Hindi and Bengali
H = (H – B) ∪ (H ∪ B)
750 = n(H-B) + 150
n(H-B) = 600
Similarly, B = (B-H) ∪ (H ∩ B)
400 = n(B-H) + 150
n(B-H) = 400 – 150 = 250
问题14.对500名电视观众的调查得出以下信息：285个看足球，195个看曲棍球，115个看篮球，50个不看三场比赛中的任何一场。有多少人观看这三场比赛?究竟有多少人观看这三场比赛?
解决方案：
Let assume that
n(P) the number of people
n(F) the number of people who watch football
n(H) the number of people who watch hockey
n(B) the number of people who watch basketball
n(P) = 500 n(F)=285 n(H) = 195 n(B) = 115 n(F ∩ B) = 45 n(F ∩ H) = 70
n(H ∩ B) = 50 and n(F∪H ∪ B) = 50
n(F ∪ H ∪ B’) = n(P) – n(F ∪ H ∪ B)
50 = 500 – (285 + 195 +115 -70 -50 – 45)
n(F∩ H ∩ B) = 20
Number of people who watch only football = 285 – (50+20+25)
= 285 – 195 = 190
Number of people who watch only hockey = 195 – (50 +20 + 30)
= 195 – 100 = 95
Number of people who watch only basketball = 115 – (25 + 20 + 30)
= 40
Number of people who watch exactly one of the three games = Number of people who watches
either football only or basketball only.
190 + 95 + 40 = 325
问题15：在对100人的调查中，发现28读杂志A，30读杂志B，42读杂志C，B读10读10阅读的A和C杂志，5读杂志B以及阅读三本杂志。找：
(i)有多少本杂志没有读过三本?
(ii)仅读了几本C杂志?
解决方案：
Let assume that
n(P) denote the total number of person
n(A) denotes the number of the people who read magazine A
n(B) denotes the number of the people who read magazine B
n(C) denote the number of people who read magazine
n(P) = 100 n(A) = 28 n(B) = 30 n(C) = 42 n(A ∩ B) = 8
n(A ∩ C) =10, n(B ∩ C) = 5, n(A ∩ B ∩ C) = 3
According to the formula
n(A ∪ B ∪) = n(A) + n(B) + n(C) – n(A ∩ B) – n(B ∩ C) – n(A ∩ C) + n(A∩ B ∩ C)
= 28 + 30 + 42 – 8 -10 – 5 + 3
=100 – 20 = 80
Number of people who read none of the three magazine:
= n (A ∪ B ∪ C)’
= n(P) – n(A ∪ B ∪ C)
100 – 80 =20
(ii) Number people who read magazine C only:
= 42 – (& + 3 + 2)
= 30
问题16。在对100名学生的调查中，发现学习各种语言的学生人数为：仅英语18，英语但非印地语23，英语和梵语8，英语26，梵文48，梵语和印地语8，否语言24.查找有多少学生正在学习英语和北印度语?
解决方案：
n(U)=100 (Total number of students)
n(E)=26 (Number of student studying English)
n(S)=48 (Number of student studying Sanskrit)
n(E∩S)=8
n(S∩H)=8
n(E∩H∩S)=3
The number of students who study English only =18
Number of students who study no language =24
Number of students who study Hindi only =[100−(18+5+3+5+35)]−24
=100−66−24
=100−90
=10
Number of students who study Hindi =10+3+5
=18
And Number of students who study English and Hindi = 3
问题17。在调查中发现，有21个喜欢产品P1，有26个喜欢产品P3，有29个喜欢产品P1和P2，有12个喜欢产品P3和P1，有14个喜欢产品P2和P1，有8个喜欢全部在这三个产品中，找到仅P3有多少喜欢的产品?
解决方案：
Let assume that A, B, and C be the set of people who like product P1, P2, and P3 respectively.
n(A) = 21, n(B) = 26, n(C) = 29, n(A ∩ B) = 14, n(C ∩ A) = 12, n(B ∩ C) = 14, n(A ∩ B ∩ C) = 8
People who many liked product C only
= n(C) – n(C ∩ A) – n(B ∩ C) + n(A ∩ B ∩ C)
= 29 -12 – 14 + 8
= 11
Hence, 11 liked product P3 only.