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

2. •describe the set notation given by
the shaded region in the Venn
Diagram; and
•solve problems using Venn Diagram.

3. Describe the set notation given by the
shaded region.
A
AA ∩ B A ∪ B
A B A B

4. Describe the set notation given by the
shaded region.
A B
A - B (B ∪ C)
A
CB
A
CB
A ∪ B ∪ C
A ∩ B’

5. Describe the set notation given by the
shaded region.
(A ∩ B)’ (A ∪ B)’(B ∪ C) ∩ A’
A
CB
AA 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 – apple B – 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 – apple B – 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 TI 3
5 7
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 TI 3
5 7
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 TI 3
5 7
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 TI 3
5 7
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. A teacher announces that out of 30
students in class, 16 passed both
the Math and Science tests, and 24
passed the Science test.
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