Grade 7 maths questions on set theory with answers are presented. Some of these questions can be challenging and need more time to be solved. Also, the solutions and explanations are included.

1. ### Question 1

Give the cardinality of set A and B defined by
A = {a, b, c, d} and B = {1, 4, 7, 9, 10, 12, 23}

2. ### Question 2

Give the cardinality of
a) the set of all months beginning with M.
b) the set of all vowels in the English alphabet.

3. ### Question 3

Sets A and B are defined by
A = {3, 5, 7, 8} and B = {x, y, z}

a) 3 ∈ A
b) 3 ∈ B
c) x ∉ A
d) z ∈ B
e) 8 ∈ B

4. ### Question 4

List all terms in each set
a) The set of all positive even numbers less than or equal to 10
b) The set of all letters in the word "AUSTRALIA".
c) The set of all whole numbers greater than 3 and smaller than 16, and divisible by 3.
d) The set of all whole numbers greater than 5 and smaller than 35, and divisible by 5.
e) The set of all prime numbers divisible by 3.
f) The set of all numbers whose absolute value is equal to 7.

5. ### Question 5

Set A, B, C and D are defined by:
A = {2,3,4,5,6,7}
B = {3,5,7}
C = {3,5,7,20,25,30}
D = {20,25,30}
a) A ⊂ B
b) B ⊂ A
c) B ⊄ C
d) C ⊂ D
e) D ⊄ A

6. ### Question 6

Use set A, B, C and D defined in question 5 to find
a) A ⋃ B
b) A ⋂ B
c) B ⋂ C
d) C ⋃ B
e) D ⋂ C
f) (A ⋂ B) ⋂ C
g) (A ⋃ B) ⋂ (C ⋃ D)
h) (A ⋃ B) ⋃ (C ⋃ D)

## Answers to the Above Questions

1. Card(A) = 4 , Card(B) = 7
2. a) 2
b) 5
3. a) true
b) false
c) false
d) true
e) false
4. a) {2,4,6,8,10}
b) {A,U,S,T,R,L,I}
c) {6,9,12,15}
d) {10,15,20,25,30}
e) {3}
f) {-7,7}
5. a) false
b) true
c) false
d) false
e) true
6. a) A ⋃ B = A
b) A ⋂ B = B
c) B ⋂ C = B
d) C ⋃ B = C
e) D ⋂ C = D
f) (A ⋂ B) ⋂ C = B
g) (A ⋃ B) ⋂ (C ⋃ D) = B
h) (A ⋃ B) ⋃ (C ⋃ D) = {2,3,4,5,6,7,20,25,30}