Name ________________________________
Principle of Inclusion Practice
1) How many integers from 1 – 100 are divisible by:
a.
b.
c.
d.
6
8
13
19
2) How many integers from 1 – 1000 are divisible by 5 or 8?
3) How many integers from 1 – 1000 are divisible by 3, 5, or 7?
4) There are 65 students taking Algebra II, 50 students taking Discrete Math, and 20 students
taking Algebra II and Discrete Math. How many students are in either Algebra II or Discrete
Math? (no venn diagram)
5) Given the following information, how many people like Math, Science, or Social Studies? (no
Venn diagram).
56 like Math
18 like Math and Science
43 like Science
10 like Science and Social Studies
35 like Social Studies
12 like Math and Social Studies
6 like all three subjects
6) Let A and B be sets such that |AUB| = 20, |B| = 10 and |A∩B|=5. How many elements are in set A?
7) A physical education class was asked which of 3 types of exercise they liked. All students had to
choose at least one. Twenty-five students chose jogging, 20 selected basketball, and 15 liked to swim.
Ten play basketball and jog, 5 play basketball and swim, 7 jog and swim and 2 people do all 3. How
many students took the survey? (no venn diagram)
8) A survey of a group of students, revealed that 60 of them liked at least one of the cereals,
Frosted Flakes or Lucky Charms. If 50 of them liked Frosted Flakes and 46 of them liked Lucky
Charms, how many students
a) liked both cereals?
b) liked Frosted Flakes but did not like Lucky Charms?
9) In a survey of 68 students, 62 like the Steelers, 42 liked the Pirates, and 55 liked the
Penguins. 32 of them liked all 3 teams, 39 liked both the Steelers and Pirates, 35 liked both the
Pirates and Penguins. All student surveyed liked at least one team. How many liked both the
Steelers and Penguins?
10) In a survey of 70 students on Movie preferences, the students were asked whether they
liked the movies “Star Wars” and “Frozen”. (All students had seen both movies and the only
options for answers were like/dislike.) 50 of the students said they liked “Star Wars” and 25 of
them said they didn’t like “Frozen”. All students liked at least one of the movies. How many
students said they liked both movies?