EduSahara™ Worksheet

Question 1

1.

If A = {7,15,11,13,2,9} , B = {5,15,8,14,4,10} and C = {6,8,1,7,3,10}, then A ∩ (B ∩ C) =

(i)

{6}
(ii)

{}
(iii)

{16}
(iv)

{13}
(v)

{4}

Question 2

2.

If μ = {-9,16,8,9,6,4,-8,15,-7,-2,12,1,-4,13,-3,2,7,-5,5,-1,11,14,10,0},A = {-9,16,8,9,6,4,-8,15}, B = {-7,-2,-9,15,9,16,6,12,1}, C = {-4,13,-9,1,4,-3,2,-7}, find A − (B ∪ C)

(i)

{8}
(ii)

{8,-8}
(iii)

{-8}
(iv)

{8,-8,-5}
(v)

{-8,-5}

Question 3

3.

If μ = {-1,9,-5,5,-7,1,14,13,-9,-3,-4,12,3,0,8,16,-6,2,-2,6,4,15,11},A = {-1,9,-5,5,-7,1}, B = {14,9,13,-7,-9,-3,5,-5,-4,12}, C = {5,3,0,8,1,14,-7,13,16,-6}, find A ∪ (B ∩ C)

(i)

{-5,-7,9,5,13,14,1}
(ii)

{-5,-1,-7,9,5,13,1}
(iii)

{-5,-1,-7,9,5,13,14,1}
(iv)

{-5,-1,-7,9,5,13,1,6}
(v)

{-5,-1,-7,9,5,13,14,1,6}

Question 4

4.

If μ = {8,-2,3,6,5,-7,-3,1,-9,-8,-5,-1,-6,7,2}, A = {8,-2,3,6,5} and B = {-7,6,8,-3,1,-9,-8}, find (A ∩ B)'

(i)

{}
(ii)

{5,-5,3,-1,-3,-2,7,-9,2,-6,1,-8}
(iii)

{-7,-3,-9,-1,7,5,1,-8,-2,2,-5,-6}
(iv)

{5,2,-5,-7,3,-2,-8,7,-6,-3,-1,1,-9}
(v)

{-6,-1,-8,-7,2,-2,3,-5,-3,-9,5,7}

Question 5

5.

Which of the following is 'not a subset' symbol?

(i)

⊆
(ii)

⊅
(iii)

⊃
(iv)

∈
(v)

⊄

Question 6

6.

Which of the following is 'superset' symbol?

(i)

∪
(ii)

⊃
(iii)

⊆
(iv)

↔
(v)

⊅

Question 7

7.

If μ = {6,7,11,8,12,-7,9,2,16,14,-2,5,-8,-6,-5,13,1,-3,15,-4,-1,10},A = {6,7,11,8,12,-7,9}, B = {2,6,16,14,-2,5,-8,-6}, C = {-5,16,-8,13,7,5,14,1,-3,-7}, find B − (A ∩ (B ∩ C))

(i)

{6,2,5,-8,16,14,-2}
(ii)

{6,2,5,-8,16,14,-6,-2,-4}
(iii)

{6,2,5,-8,16,14,-6,-2}
(iv)

{6,2,5,16,14,-6,-2,-4}
(v)

{6,2,5,16,14,-6,-2}

Question 8

8.

If μ = {-4,-9,-8,-6,-7,7,-3,2,0,9,1,4,-1,-5}, A = {-4,-9,-8,-6,-7,7,-3} and B = {2,-4,0}, find (A − B)'

(i)

{}
(ii)

{4,9,0,-1,-5,-4,1}
(iii)

{-4,-5,-1,2,0,4,1,9}
(iv)

{2,0,-4,-5,1,4,-1}

Question 9

9.

Which of the following are true?

a)	A ∩ A' = μ
b)	A ∩ A' = A
c)	A ∪ A' = μ
d)	A ∩ A' = ∅
e)	A ∪ A' = A
f)	A ∪ A' = ∅

(i)

{b,d}
(ii)

{a,c}
(iii)

{c,d}
(iv)

{a,d,c}
(v)

{e,f,c}

Question 10

10.

Which of the following is 'intersection' symbol?

(i)

⊃
(ii)

∩
(iii)

↔
(iv)

⊆
(v)

⊂

Question 11

11.

If μ = {2,-4,1,17,-8,-3,-5,8,6,3,14,9,-1,12,11,5,7,-7,0,15,10,18,-2},A = {2,-4,1,17,-8,-3,-5,8,6}, B = {3,14,17,9,-1,12,11,5}, C = {7,11,3,-4,-8,-7,14,17,-3,0}, find (C ∩ A)'

(i)

{2,18,-2,11,-1,8,0,-5,9,12,10,1,5,7,14,15,-7,6}
(ii)

{2,18,-2,11,-1,8,0,-5,9,12,10,1,5,7,14,15,-7,6,-4}
(iii)

{2,18,-2,11,-1,8,0,-5,9,12,10,1,5,7,14,15,-7,3,6}
(iv)

{2,18,-2,11,-1,8,0,-5,9,12,10,1,5,7,14,15,-7,3,6,-4}
(v)

{2,18,-2,11,-1,8,0,-5,9,12,10,1,7,14,15,-7,3,6}

Question 12

12.

Which of the following are null sets?

a)

{}

b)

∅

c)

{∅}

d)

{empty}

e)

{5,8,2}

(i)

{d,b}
(ii)

{e,c,a}
(iii)

{a,b}
(iv)

{c,a}
(v)

{d,b,a}

Question 13

13.

If μ = {-7,-5,-3,-8,4,8,1,2,3,10,-2,-6,5,6,-1,7,-4,-9}, A = {-7,-5,-3,-8,4,8,1} and B = {2,1,3,10,-2,-8,8}, find A ∩ B

(i)

{8,-8,1}
(ii)

{}
(iii)

{6,1,8}
(iv)

{-8,-9,8,1}
(v)

{1,8}

Question 14

14.

If μ = {7,0,3,6,-4,5,8,4,2,-9,-8,-6,-3}, A = {7,0,3,6,-4} and B = {5,8,6,4,3}, find n((B − A)')

(i)

9
(ii)

10
(iii)

13
(iv)

11
(v)

7

Question 15

15.

If A = {11,7,2} , B = {4,0,8} and C = {1,15,2,14} , then B ∪ (C ∪ A) =

(i)

{15,4,1,2,0,11,14,8}
(ii)

{0,2,11,4,8,7,14,15}
(iii)

{15,4,2,11,8,14,7,1}
(iv)

{2,15,11,0,14,1,4,7,8}
(v)

{11,8,4,7,1,2,0,14,19,15}

Question 16

16.

If μ = {5,6,4,15,-8,-6,-3,-2,14,-1,13,-4,-5,9,-9,11,8,7,12,0},A = {5,6,4,15,-8,-6,-3,-2}, B = {-2,14,-1,13,15,-4}, C = {-5,4,9,-9,-6,6,15,-3,11,8}, find (B ∩ C)'

(i)

{8,13,-5,4,5,11,-6,14,9,6,-4,-9,7,-8,-1,0,-3,12,-2}
(ii)

{8,13,-5,4,5,11,-6,14,9,6,-9,7,-8,-1,0,-3,12,-2,15}
(iii)

{8,13,-5,4,5,11,-6,14,9,6,-9,7,-8,-1,0,-3,12,-2}
(iv)

{8,13,-5,4,5,11,-6,14,9,6,-4,-9,7,-8,-1,0,-3,12,-2,15}
(v)

{8,13,-5,4,5,11,14,9,6,-4,-9,7,-8,-1,0,-3,12,-2}

Question 17

17.

If μ = {-9,2,3,-8,5,-4,-1,8,-7,-3,7,6,-2,0,9,-6}, A = {-9,2,3,-8,5,-4,-1} and B = {2,8,-1,-7,3}, find B − A

(i)

{8,-6}
(ii)

{}
(iii)

{8,-7}
(iv)

{-6,-7,8}
(v)

{-7}

Question 18

18.

If μ = {10,18,16,2,-5,-6,3,9,11,-3,-1,17,-2,4,14,-7,-9,8,-4,13,1,6,0,7,5},A = {10,18,16,2,-5,-6,3,9,11,-3}, B = {18,-1,17,11,3,-2,16,2,4,10}, C = {14,-5,-7,-9,3,8,-4,10,-6}, find A ∩ B ∩ C

(i)

{10,3,2}
(ii)

{10}
(iii)

{10,3}
(iv)

{10,2}
(v)

{10,8}

Question 19

19.

Which of the following is a null set?

(i)

{-5,-8,0,7}
(ii)

{}
(iii)

{5,9,-6,3,8}
(iv)

{1,3}
(v)

{-2,-4,-9}

Question 20

20.

Which of the following are disjoint sets?

(i)
{17,8,14,18,16,1}

,

{18,9,1,8,10}
(ii)
{17,8,14,18,16,1}

,

{}
(iii)
{}

,

{17,8,14,18,16,1}
(iv)
{17,14,16}

,

{9,1,10}
(v)
{17,8,14,18,16,1}

,

{17,8,14,18,16,1}

Question 21

21.

If μ = {11,10,13,-1,-2,-9,3,-5,-4,12,-8,2,-3,-7,4,9,0,1,7,5},A = {11,10,13,-1,-2,-9,3}, B = {-5,-4,12,-8,2,13,10,-3,-7}, C = {10,4,-2,9,-1,0}, find (A ∩ B)'

(i)

{3,12,11,-9,-3,-1,-4,-7,7,-8,0,4,9,1,-5,-2,5}
(ii)

{3,12,11,-9,-3,-1,-4,-7,7,2,-8,0,4,9,1,-5,-2,5}
(iii)

{3,12,11,-9,-3,-1,-4,-7,7,2,-8,0,4,1,-5,-2,5}
(iv)

{3,12,11,-9,-3,-1,-4,-7,7,2,-8,0,4,9,1,-5,-2,5,13}
(v)

{3,12,11,-9,-3,-1,-4,-7,7,2,-8,0,4,1,-5,-2,5,13}

Question 22

22.

If μ = {4,-1,-4,8,-8,-2,1,-9,6,3,9,-3,-7,5,-5,2,7}, A = {4,-1,-4,8,-8,-2,1} and B = {-9,-8,6,8,-2,3}, find n(A')

(i)

12
(ii)

11
(iii)

10
(iv)

8
(v)

9

Question 23

23.

Find the number of proper subsets of A = {1,0,4}

(i)

4
(ii)

10
(iii)

6
(iv)

7
(v)

8

Question 24

24.

For any two non-empty sets A and B, which of the following are true?

a)	A ∩ B = B ∪ A
b)	A ∪ B = ∅
c)	A ∪ B = B ∩ A
d)	A ∩ B = B ∩ A
e)	A ∪ B = B ∪ A

(i)

{a,d}
(ii)

{c,a,d}
(iii)

{d,e}
(iv)

{b,e,d}
(v)

{b,e}

Question 25

25.

If A = {8,3,9,10} , B = {5,10,2} and C = {13,4,5} , then A ∪ (B ∪ C) =

(i)

{8,10,9,3,5,4,2}
(ii)

{5,2,10,3,13,9,8,4}
(iii)

{4,3,5,9,10,8,13}
(iv)

{13,16,9,10,3,5,8,2,4}
(v)

{4,5,8,10,2,3,13}

Assignment Key