Scroll:Theory of sets >> set operations using venn diagram >> ps (4163)


Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.



 

1)  

 If n(A) = 16,n(B) = 19,n(AUB) = 24, n(A') = 13, Find n(A∩B) and n(U).

A
B
16
19
24
 

 n(A∩B) =

 n(U) =



Answer:_______________




2)  

 If n(A) = 22,n(B) = 20,n(AUB) = 28, n(A') = 14, Find n(A∩B) and n(U).

A
B
22
20
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




3)  

 If n(A) = 18,n(B) = 14,n(AUB) = 28, n(A') = 13, Find n(A∩B) and n(U).

A
B
18
14
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




4)  

 If n(A) = 24,n(B) = 19,n(AUB) = 27, n(A') = 13, Find n(A∩B) and n(U).

A
B
24
19
27
 

 n(A∩B) =

 n(U) =



Answer:_______________




5)  

 If n(A) = 22,n(B) = 23,n(AUB) = 21, n(A') = 19, Find n(A∩B) and n(U).

A
B
22
23
21
 

 n(A∩B) =

 n(U) =



Answer:_______________




6)  

 If n(A) = 23,n(B) = 18,n(AUB) = 29, n(A') = 18, Find n(A∩B) and n(U).

A
B
23
18
29
 

 n(A∩B) =

 n(U) =



Answer:_______________




7)  

 If n(A) = 17,n(B) = 12,n(AUB) = 26, n(A') = 15, Find n(A∩B) and n(U).

A
B
17
12
26
 

 n(A∩B) =

 n(U) =



Answer:_______________




8)  

 If n(A) = 19,n(B) = 16,n(AUB) = 26, n(A') = 14, Find n(A∩B) and n(U).

A
B
19
16
26
 

 n(A∩B) =

 n(U) =



Answer:_______________




9)  

 If n(A) = 25,n(B) = 17,n(AUB) = 20, n(A') = 19, Find n(A∩B) and n(U).

A
B
25
17
20
 

 n(A∩B) =

 n(U) =



Answer:_______________




10)  

 If n(A) = 26,n(B) = 19,n(AUB) = 28, n(A') = 15, Find n(A∩B) and n(U).

A
B
26
19
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




 

1)  

 If n(A) = 16,n(B) = 19,n(AUB) = 24, n(A') = 13, Find n(A∩B) and n(U).

A
B
16
19
24
 

 n(A∩B) = Answer: 11

 n(U) = Answer: 29


SOLUTION 1 :

 n(A) = 16,

n(B) = 19,

n(AUB) = 24,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

24 = 16 + 19 - n(A∩B)  

24 = 35 - n(A∩B)  

n(A∩B) = 35 - 24  

n(A∩B) = 11

HInt n(U) = n(A) + n(A")

n(U) = 16 + 13

 n(U) = 29



2)  

 If n(A) = 22,n(B) = 20,n(AUB) = 28, n(A') = 14, Find n(A∩B) and n(U).

A
B
22
20
28
 

 n(A∩B) = Answer: 14

 n(U) = Answer: 36


SOLUTION 1 :

 n(A) = 22,

n(B) = 20,

n(AUB) = 28,

n(A") = 14

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 22 + 20 - n(A∩B)  

28 = 42 - n(A∩B)  

n(A∩B) = 42 - 28  

n(A∩B) = 14

HInt n(U) = n(A) + n(A")

n(U) = 22 + 14

 n(U) = 36



3)  

 If n(A) = 18,n(B) = 14,n(AUB) = 28, n(A') = 13, Find n(A∩B) and n(U).

A
B
18
14
28
 

 n(A∩B) = Answer: 4

 n(U) = Answer: 31


SOLUTION 1 :

 n(A) = 18,

n(B) = 14,

n(AUB) = 28,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 18 + 14 - n(A∩B)  

28 = 32 - n(A∩B)  

n(A∩B) = 32 - 28  

n(A∩B) = 4

HInt n(U) = n(A) + n(A")

n(U) = 18 + 13

 n(U) = 31



4)  

 If n(A) = 24,n(B) = 19,n(AUB) = 27, n(A') = 13, Find n(A∩B) and n(U).

A
B
24
19
27
 

 n(A∩B) = Answer: 16

 n(U) = Answer: 37


SOLUTION 1 :

 n(A) = 24,

n(B) = 19,

n(AUB) = 27,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

27 = 24 + 19 - n(A∩B)  

27 = 43 - n(A∩B)  

n(A∩B) = 43 - 27  

n(A∩B) = 16

HInt n(U) = n(A) + n(A")

n(U) = 24 + 13

 n(U) = 37



5)  

 If n(A) = 22,n(B) = 23,n(AUB) = 21, n(A') = 19, Find n(A∩B) and n(U).

A
B
22
23
21
 

 n(A∩B) = Answer: 24

 n(U) = Answer: 41


SOLUTION 1 :

 n(A) = 22,

n(B) = 23,

n(AUB) = 21,

n(A") = 19

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

21 = 22 + 23 - n(A∩B)  

21 = 45 - n(A∩B)  

n(A∩B) = 45 - 21  

n(A∩B) = 24

HInt n(U) = n(A) + n(A")

n(U) = 22 + 19

 n(U) = 41



6)  

 If n(A) = 23,n(B) = 18,n(AUB) = 29, n(A') = 18, Find n(A∩B) and n(U).

A
B
23
18
29
 

 n(A∩B) = Answer: 12

 n(U) = Answer: 41


SOLUTION 1 :

 n(A) = 23,

n(B) = 18,

n(AUB) = 29,

n(A") = 18

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

29 = 23 + 18 - n(A∩B)  

29 = 41 - n(A∩B)  

n(A∩B) = 41 - 29  

n(A∩B) = 12

HInt n(U) = n(A) + n(A")

n(U) = 23 + 18

 n(U) = 41



7)  

 If n(A) = 17,n(B) = 12,n(AUB) = 26, n(A') = 15, Find n(A∩B) and n(U).

A
B
17
12
26
 

 n(A∩B) = Answer: 3

 n(U) = Answer: 32


SOLUTION 1 :

 n(A) = 17,

n(B) = 12,

n(AUB) = 26,

n(A") = 15

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

26 = 17 + 12 - n(A∩B)  

26 = 29 - n(A∩B)  

n(A∩B) = 29 - 26  

n(A∩B) = 3

HInt n(U) = n(A) + n(A")

n(U) = 17 + 15

 n(U) = 32



8)  

 If n(A) = 19,n(B) = 16,n(AUB) = 26, n(A') = 14, Find n(A∩B) and n(U).

A
B
19
16
26
 

 n(A∩B) = Answer: 9

 n(U) = Answer: 33


SOLUTION 1 :

 n(A) = 19,

n(B) = 16,

n(AUB) = 26,

n(A") = 14

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

26 = 19 + 16 - n(A∩B)  

26 = 35 - n(A∩B)  

n(A∩B) = 35 - 26  

n(A∩B) = 9

HInt n(U) = n(A) + n(A")

n(U) = 19 + 14

 n(U) = 33



9)  

 If n(A) = 25,n(B) = 17,n(AUB) = 20, n(A') = 19, Find n(A∩B) and n(U).

A
B
25
17
20
 

 n(A∩B) = Answer: 22

 n(U) = Answer: 44


SOLUTION 1 :

 n(A) = 25,

n(B) = 17,

n(AUB) = 20,

n(A") = 19

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

20 = 25 + 17 - n(A∩B)  

20 = 42 - n(A∩B)  

n(A∩B) = 42 - 20  

n(A∩B) = 22

HInt n(U) = n(A) + n(A")

n(U) = 25 + 19

 n(U) = 44



10)  

 If n(A) = 26,n(B) = 19,n(AUB) = 28, n(A') = 15, Find n(A∩B) and n(U).

A
B
26
19
28
 

 n(A∩B) = Answer: 17

 n(U) = Answer: 41


SOLUTION 1 :

 n(A) = 26,

n(B) = 19,

n(AUB) = 28,

n(A") = 15

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 26 + 19 - n(A∩B)  

28 = 45 - n(A∩B)  

n(A∩B) = 45 - 28  

n(A∩B) = 17

HInt n(U) = n(A) + n(A")

n(U) = 26 + 15

 n(U) = 41