EduSahara™ Worksheet

Question 1

1.

Which of the following are true?

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

(i)

{d,e,a}
(ii)

{d,a}
(iii)

{d,f,c}
(iv)

{a,b,c,e}
(v)

{f,b}

Question 2

2.

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

(i)

{3,-7,4,-1,-4,-8,-2,10}
(ii)

{-7,4,-1,-4,-8,-2}
(iii)

{-7,4,-1,-4,-8,-2,10}
(iv)

{3,4,-1,-4,-8,-2}
(v)

{3,-7,4,-1,-4,-8,-2}

Question 3

3.

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

(i)

{8,0,-7,-3}
(ii)

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

{2,-3,0,8,-7,-6}
(iv)

{-3,-7,8,0,-6}
(v)

{-6,-3,-7,0}

Question 4

4.

If A = {7,12,5} , B = {5,0,10} and C = {1,5,11} , then A ∪ (B ∪ C) =

(i)

{10,11,5,7,12,0}
(ii)

{0,5,10,11,7,1}
(iii)

{11,0,5,1,12,7}
(iv)

{5,1,12,11,10,0,7,16}
(v)

{12,11,5,7,10,1,0}

Question 5

5.

If A ⊂ B, then which of the following are true?

a)	A' ⊂ B
b)	B ⊂ A
c)	A' = B
d)	B ⊃ A
e)	A = B

(i)

{b,d}
(ii)

{c,e,d}
(iii)

{a,d}
(iv)

{d}

Question 6

6.

Which of the following is 'superset' symbol?

(i)

∩
(ii)

↔
(iii)

∉
(iv)

⊃
(v)

∪

Question 7

7.

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

(i)

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

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

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

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

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

Question 8

8.

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

(i)

8
(ii)

12
(iii)

9
(iv)

6
(v)

10

Question 9

9.

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

(i)

2
(ii)

1
(iii)

0
(iv)

5
(v)

3

Question 10

10.

If A and B are disjoint sets, which of the following are true?

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

(i)

{c,d,e}
(ii)

{b,e}
(iii)

{e}
(iv)

{a,e}

Question 11

11.

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

(i)

{-9,0,-6,4,-1,-4}
(ii)

{-4,-1,4,0,9,-6}
(iii)

{}
(iv)

{-6,-9,4,0,9,-1,-4}

Question 12

12.

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

(i)

{-2,4,9,8,-4}
(ii)

{8,-2,-4,9,5,4}
(iii)

{}
(iv)

{-2,9,4,5,-4}

Question 13

13.

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

(i)

{10}
(ii)

{4}
(iii)

{19}
(iv)

{13}
(v)

{}

Question 14

14.

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

(i)

{14,-7,17,16,1,-2}
(ii)

{14,-7,17,16,1}
(iii)

{14,-7,17,16}
(iv)

{14,-7,16,1,-2}
(v)

{14,-7,16,1}

Question 15

15.

Which of the following is superset of A = {4,9,6,0}?

(i)

{4,0,7,6}
(ii)

{4,9,6,3,0}
(iii)

{9,6}
(iv)

{6,0,1,9}
(v)

{6,4,9}

Question 16

16.

Which of the following is equal to set A = {0,-3,-7,7}?

(i)

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

{-3,7,-7,0}
(iii)

{-3,5,-8,-7,7}
(iv)

{7,-2,9}
(v)

{-1,-5,5,-4}

Question 17

17.

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

(i)

{17,-7,10,1,4,11,-3,-9,2,13,-5,0}
(ii)

{17,-7,10,1,4,-3,-9,2,13,-5,0,12}
(iii)

{17,-7,10,1,4,-3,-9,2,13,-5,0}
(iv)

{17,-7,10,1,4,11,-3,-9,2,13,-5,0,12}
(v)

{-7,10,1,4,11,-3,-9,2,13,-5,0}

Question 18

18.

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

(i)

{13,15,12,9,-6,-8,7,4,1,16,-2}
(ii)

{13,15,12,9,-8,7,4,1,16,-2}
(iii)

{13,15,12,9,-6,-8,4,1,16}
(iv)

{13,15,12,9,-6,-8,7,4,1,16}
(v)

{13,15,12,9,-8,7,4,1,16}

Question 19

19.

If A = {9,6,2,0} and B = {9,3,4,8} , then A ∪ B =

(i)

{8,2,0,6,3,4}
(ii)

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

{2,9,8,6,4,3}
(iv)

{11,4,9,2,0,3,6,8}
(v)

{0,4,2,9,13,3,6}

Question 20

20.

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

(i)

{-5,10,-4,15,-7}
(ii)

{-5,10,-4,-7,-1}
(iii)

{-5,10,-4,15,-7,-1}
(iv)

{-5,10,15,-7}
(v)

{-5,10,-4,-7}

Question 21

21.

Which of the following is 'subset or equal to' symbol?

(i)

⊆
(ii)

∩
(iii)

⊇
(iv)

∉
(v)

∪

Question 22

22.

Which of the following is equivalent set of A = {6,0}?

(i)

{-9,4,-5,3}
(ii)

{4,-8}
(iii)

{}
(iv)

{6}
(v)

{4,-8,0}

Question 23

23.

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

(i)

{-6,13,12,-3,9,11,5,6,-5,7,14,10,-7,4}
(ii)

{-6,13,12,-3,9,11,5,6,-5,7,14,10,-7}
(iii)

{-6,13,12,-3,9,11,5,6,-5,7,10,-1,-7}
(iv)

{-6,13,12,-3,9,11,5,6,-5,7,14,10,-1,-7}
(v)

{-6,13,12,-3,9,11,5,6,-5,7,14,10,-1,-7,4}

Question 24

24.

If A = {7,3,0,9} and B = {7,5,10,8} , then B ∪ A =

(i)

{7,8,9,5,3,10,0}
(ii)

{0,12,5,3,7,8,10,9}
(iii)

{8,0,3,10,5,9}
(iv)

{7,0,10,8,9,5}
(v)

{10,9,13,5,8,3,0}

Question 25

25.

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

(i)

5
(ii)

8
(iii)

4
(iv)

2
(v)

6

Assignment Key