Solving Problems Using Venn Diagram

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1. Grade 7 –Mathematics
Quarter I
SOLVING PROBLEMS
USING VENN DIAGRAM

2. •describethesetnotationgivenby
theshadedregionintheVenn
Diagram;and
•solveproblemsusingVennDiagram.

3. Describethesetnotationgivenbythe
shadedregion.
A
AA ∩B A ∪B
A B A B

4. Describethesetnotationgivenbythe
shadedregion.
A B
A -B (B ∪C)
A
CB
A
CB
A ∪B∪C
A ∩B’

5. Describethesetnotationgivenbythe
shadedregion.
(A ∩B)’ (A ∪B)’(B∪C) ∩A’
A
CB
A
A B A B

6. INTERSECTION
SOLVING
PROBLEMS
USING
VENN
DIAGRAM
UNION DIFFERENCE
COMPLEMENT
“and”
“or”
“neither-nor”
“but not”
“all three”
“neither”
“only”
“but not”

7. Let’s try!
1.apple and banana
2.apple or banana
3.apple only
4.apple
A–apple B–banana
∩A B
∪A B
−A B
A
n(A ∩B)
n(A ∪B)
n(A −B)
n(A)

8. 5. apple and banana but not orange
6. neither of the three
A–appleB–banana O-orange
∩A B
A∪B∪O
n(A ∩B) −O
n(A∪B∪O)’
− O
n(A ∩B)∩O’
′

9. 7. all three
8. banana or orange but not apple
A–appleB–banana O-orange
B
n(B ∪O) ∩A’
∩ n(A ∩B ∩O)
O A∪ −
n(B ∪O) -A

10. Forty people are asked about the social media
accounts that they have.
Let F = {people who have Facebook accounts}
T = {people who have Twitter accounts}
I = {people who have Instagram accounts}
How many people have:
1. Facebook accounts?
U
F
8
6 TI3
57
4
2
n (F) = 8 + 7 + 5 + 2
n (F) = 22
2. Facebook and Twitter accounts?
n (F ∩T) = 7 + 2
n (F ∩T) = 9
U = 40 people

11. Forty people are asked about the social media
accounts that they have.
How many people have:
3. Facebook or Instagram accounts?
U
F
8
6 TI3
57
4
2
n (F ∪I) = 8 + 7 + 5 + 2 + 4 + 3
n (F ∪I) = 29
4. Twitter and Instagram accounts?
n (T ∩I) = 2 + 4
n (T ∩I) = 6
5. Facebook or Twitter accounts?
n (F ∪T) = 8 + 7 + 5 + 2 + 4 + 6
n (F ∪T) = 32

12. Forty people are asked about the social media
accounts that they have.
How many people have:
6. Facebook accounts only
U
F
8
6 TI3
57
4
2
n (F –T –I) = 8
7. Twitter and Instagram but not
Facebook accounts?
n (T ∩I) -F = 4
8. Facebook or Twitter but not Instagram accounts?
n (F ∪T) –I = 8 + 7 + 6
n (F ∪T) –I = 21

13. Forty people are asked about the social media
accounts that they have.
Let F = {people who have Facebook accounts}
T = {people who have Twitter accounts}
I = {people who have Instagram accounts}
How many people have:
9. all three?
U
F
8
6 TI3
57
4
2
n (F ∩T ∩I) = 2
10. neither one of three?
n (F ∪T ∪I)’ = 5
U = 40 people
n (F ∪T ∪I) = 8 + 7 + 5 + 2 + 4 + 3 + 6 = 35
5

14. Ateacherannouncesthatoutof30
studentsinclass,16passedboth
theMathandSciencetests,and24
passedtheSciencetest.
U
Math Science
16
8
1. How many passed the Math test
only?
6
2. How many passed the Science test only?
3. How many students did not pass either Math or
Science test?
n (M –S) = 0
n (S –M) = 8
n (M ∪S)’ = 6