EduSahara™ Worksheet

Question 1

1.

Which of the following are true?

a)	(A ∩ B) ∩ C = A ∩ (B ∩ C)
b)	A ∪ (B ∩ C) = (A ∩ B) ∪ (A ∩ C)
c)	A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
d)	A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
e)	(A ∪ B) ∪ C = A ∪ (B ∪ C)
f)	A ∩ (B ∪ C) = (A ∪ B) ∩ (A ∪ C)

(i)

{a,c,d,e}
(ii)

{b,e,a}
(iii)

{f,c}
(iv)

{b,a}
(v)

{b,f,d}

Question 2

2.

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

(i)

9
(ii)

4
(iii)

7
(iv)

6
(v)

5

Question 3

3.

If A = {5,12,9} , B = {13,15,5} and C = {1,15,6,4} , then B ∪ (C ∪ A) =

(i)

{5,9,6,13,1,12,15}
(ii)

{9,6,12,18,5,1,4,13,15}
(iii)

{9,5,1,15,6,12,4}
(iv)

{9,4,6,15,1,5,13}
(v)

{1,9,4,12,15,6,13,5}

Question 4

4.

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

(i)

12
(ii)

13
(iii)

16
(iv)

15
(v)

14

Question 5

5.

If μ = {11,3,-4,-1,1,-2,-3,5,13,-6,-8,9,10,8,0,7,12,-7,4},A = {11,3,-4,-1,1,-2,-3}, B = {-3,5,13,-1,-6,-4,-8}, C = {11,-1,9,-3,10,-2,13,3}, find C ∩ A

(i)

{11,3,-1,-2,7}
(ii)

{3,-1,-3,-2,-6}
(iii)

{11,3,-1,-2}
(iv)

{11,3,-1,-3,-2}
(v)

{11,3,-1,-3,-2,7}

Question 6

6.

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

(i)

{-1,-8,-6,7,-4,-3,1,-7,-5,14,-9,9}
(ii)

{-1,-8,-6,7,-4,-3,1,-7,-5,14,-9}
(iii)

{-1,-8,-6,7,-4,-3,1,-7,-5,14}
(iv)

{-1,-8,-6,7,-4,-3,1,-7,-5,14,9}
(v)

{-1,-8,7,-4,-3,1,-7,-5,14,-9}

Question 7

7.

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

(i)

{3,9,-8,6,-9}
(ii)

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

{10,9,-8,-9,3,6}
(iv)

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

{6,-9,-10,5,10,3}

Question 8

8.

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

(i)

∉
(ii)

⊄
(iii)

⊇
(iv)

∈
(v)

⊅

Question 9

9.

If A = {0,2,3,9,4} and B = {6,10,2,4,9} , then B ∩ A =

(i)

{9,2,4}
(ii)

{9,2,11,4}
(iii)

{10,2,4,0,9}
(iv)

{9,6,2,4}
(v)

{2,0,4,9}

Question 10

10.

If A = {4,-9,-7,-3,-4,-5} and μ = {4,-9,-7,-3,-4,-5,8,2,-8,0}, find A ∪ A'

(i)

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

{-4,-8,2,4,-3,8,-9,-6,0,-7}
(iii)

{-4,-5,-8,4,3,-1,1,8,-7,-9}
(iv)

{4,2,-4,-8,-3,0,-9,-7,-5}
(v)

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

Question 11

11.

If μ = {-2,0,8,-9,-4,2,-7,7,1,3,6,9,10,5,-1,-6,-5}, A = {-2,0,8,-9,-4,2,-7} and B = {-7,7,1,0,3,-2,6}, find n(B')

(i)

11
(ii)

9
(iii)

10
(iv)

7
(v)

13

Question 12

12.

If A = {2,11,6,4,12,9,8} , B = {15,13,11,4,7,9,5} and C = {9,4,0,10,12,3,1}, then B ∩ (C ∩ A) =

(i)

{4,9,8}
(ii)

{9,7,4}
(iii)

{4,10,9}
(iv)

{4,9}
(v)

{19,9,4}

Question 13

13.

If A = {1,5,10} , B = {3,0,11} and C = {9,1,11} , then B ∪ (C ∪ A) =

(i)

{0,3,9,1,10,5,11}
(ii)

{1,3,0,9,10,17,11,5}
(iii)

{1,0,11,5,3,10}
(iv)

{9,1,5,11,3,10}
(v)

{3,10,1,9,0,11}

Question 14

14.

If A = {9,1,5,2,10} and B = {5,3,4,2,6} , then A ∩ B =

(i)

{5,2,3}
(ii)

{5,2}
(iii)

{5,2,1}
(iv)

{2,5,9,4}
(v)

{12,5,2}

Question 15

15.

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

(i)

{9,-6,14,12,10,2,13,8,-3,6,4,7,-8,3,-5,1,-2,-4}
(ii)

{9,-6,12,10,2,13,8,-3,6,4,7,5,-8,3,-5,1,-2,-4}
(iii)

{9,-6,12,10,2,13,8,-3,6,4,7,5,-8,3,-5,1,-2,-4,-7}
(iv)

{9,-6,14,12,10,2,13,8,-3,6,4,7,5,-8,3,-5,1,-2,-4,-7}
(v)

{9,-6,14,12,10,2,13,8,-3,6,4,7,5,-8,3,-5,1,-2,-4}

Question 16

16.

If μ = {-8,16,17,10,-4,0,4,-3,-7,-1,3,13,12,6,2,1,-5,15,-2,9,14,-6,-9,11},A = {-8,16,17,10,-4,0,4,-3,-7,-1}, B = {3,13,-3,-7,12,6,2,-8,10,-4}, C = {3,6,1,4,-5,16,-1}, find C ∪ A

(i)

{17,10,4,0,-4,1,-3,6,-8,16,-7,-5,-1,3}
(ii)

{17,10,4,0,1,-3,6,-8,16,-7,-5,-1,3}
(iii)

{17,10,4,0,-4,1,-3,6,-8,16,-7,-5,3}
(iv)

{17,10,4,0,-4,1,-3,6,-8,16,-7,-5,3,11}
(v)

{17,10,4,0,-4,1,-3,6,-8,16,-7,-5,-1,3,11}

Question 17

17.

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

(i)

12
(ii)

10
(iii)

9
(iv)

7
(v)

8

Question 18

18.

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

(i)

{5,-8,2,-1,0,-5,-6}
(ii)

{}
(iii)

{3,-8,0,-6,5,-1,2,-5}
(iv)

{0,3,2,-5,-1,5,-6}
(v)

{3,5,-8,-5,-6,2,0}

Question 19

19.

Which of the following are true?

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

(i)

{b,e}
(ii)

{a,e,d}
(iii)

{a,d}
(iv)

{d,e}
(v)

{c,f,d}

Question 20

20.

If μ = {6,-5,1,7,-8,5,-4,9,-3,-7,-1,8,2,11,-2,-6,0,4,3,12},A = {6,-5,1,7,-8,5,-4}, B = {9,7,-3,-7,-8,-1,-4,8}, C = {-4,2,11,6,9,-5}, find A ∪ B ∪ C

(i)

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

{9,1,-8,-7,7,-5,-4,8,-1,6,2,11,-3,5,-6}
(iii)

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

{9,1,-8,7,-5,-4,8,-1,6,2,11,-3,5}
(v)

{9,1,-8,-7,7,-5,-4,-1,6,2,11,-3,5}

Question 21

21.

Which of the following elements belong to the set {2,4,8,5,7}?

(i)

2
(ii)

16
(iii)

(-3)
(iv)

15
(v)

(-2)

Question 22

22.

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

(i)

{3,14,-2,5,2,8,7,15,0,6,16,11,-7,1,-3,-6}
(ii)

{3,14,-2,5,2,8,15,0,6,16,11,-7,1,-3,-6}
(iii)

{3,14,-2,5,2,8,7,15,0,16,11,-7,1,-3}
(iv)

{3,14,-2,5,2,8,15,0,6,16,11,-7,1,-3}
(v)

{3,14,-2,5,2,8,7,15,0,6,16,11,-7,1,-3}

Question 23

23.

Which of the following is 'universal set' symbol?

(i)

↔
(ii)

∉
(iii)

μ
(iv)

∩
(v)

⊄

Question 24

24.

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

(i)

4
(ii)

10
(iii)

6
(iv)

8
(v)

7

Question 25

25.

If A = {10,7,0,6,5} and B = {10,1,13,3,5} , then B − A =

(i)

{13,3,1,19}
(ii)

{3,13,1}
(iii)

{}
(iv)

{10,3,1,13}
(v)

{1,3}

Assignment Key