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) = 19,n(B) = 22,n(AUB) = 30, n(A') = 18, Find n(A∩B) and n(U).

A
B
19
22
30
 

 n(A∩B) =

 n(U) =



Answer:_______________




2)  

 If n(A) = 15,n(B) = 22,n(AUB) = 22, n(A') = 20, Find n(A∩B) and n(U).

A
B
15
22
22
 

 n(A∩B) =

 n(U) =



Answer:_______________




3)  

 If n(A) = 26,n(B) = 12,n(AUB) = 30, n(A') = 19, Find n(A∩B) and n(U).

A
B
26
12
30
 

 n(A∩B) =

 n(U) =



Answer:_______________




4)  

 If n(A) = 25,n(B) = 10,n(AUB) = 20, n(A') = 13, Find n(A∩B) and n(U).

A
B
25
10
20
 

 n(A∩B) =

 n(U) =



Answer:_______________




5)  

 If n(A) = 16,n(B) = 15,n(AUB) = 26, n(A') = 11, Find n(A∩B) and n(U).

A
B
16
15
26
 

 n(A∩B) =

 n(U) =



Answer:_______________




6)  

 If n(A) = 21,n(B) = 10,n(AUB) = 27, n(A') = 12, Find n(A∩B) and n(U).

A
B
21
10
27
 

 n(A∩B) =

 n(U) =



Answer:_______________




7)  

 If n(A) = 22,n(B) = 13,n(AUB) = 29, n(A') = 10, Find n(A∩B) and n(U).

A
B
22
13
29
 

 n(A∩B) =

 n(U) =



Answer:_______________




8)  

 If n(A) = 24,n(B) = 21,n(AUB) = 23, n(A') = 12, Find n(A∩B) and n(U).

A
B
24
21
23
 

 n(A∩B) =

 n(U) =



Answer:_______________




9)  

 If n(A) = 21,n(B) = 13,n(AUB) = 29, n(A') = 14, Find n(A∩B) and n(U).

A
B
21
13
29
 

 n(A∩B) =

 n(U) =



Answer:_______________




10)  

 If n(A) = 16,n(B) = 11,n(AUB) = 29, n(A') = 20, Find n(A∩B) and n(U).

A
B
16
11
29
 

 n(A∩B) =

 n(U) =



Answer:_______________




 

1)  

 If n(A) = 19,n(B) = 22,n(AUB) = 30, n(A') = 18, Find n(A∩B) and n(U).

A
B
19
22
30
 

 n(A∩B) = Answer: 11

 n(U) = Answer: 37


SOLUTION 1 :

 n(A) = 19,

n(B) = 22,

n(AUB) = 30,

n(A") = 18

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

30 = 19 + 22 - n(A∩B)  

30 = 41 - n(A∩B)  

n(A∩B) = 41 - 30  

n(A∩B) = 11

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

n(U) = 19 + 18

 n(U) = 37



2)  

 If n(A) = 15,n(B) = 22,n(AUB) = 22, n(A') = 20, Find n(A∩B) and n(U).

A
B
15
22
22
 

 n(A∩B) = Answer: 15

 n(U) = Answer: 35


SOLUTION 1 :

 n(A) = 15,

n(B) = 22,

n(AUB) = 22,

n(A") = 20

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

22 = 15 + 22 - n(A∩B)  

22 = 37 - n(A∩B)  

n(A∩B) = 37 - 22  

n(A∩B) = 15

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

n(U) = 15 + 20

 n(U) = 35



3)  

 If n(A) = 26,n(B) = 12,n(AUB) = 30, n(A') = 19, Find n(A∩B) and n(U).

A
B
26
12
30
 

 n(A∩B) = Answer: 8

 n(U) = Answer: 45


SOLUTION 1 :

 n(A) = 26,

n(B) = 12,

n(AUB) = 30,

n(A") = 19

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

30 = 26 + 12 - n(A∩B)  

30 = 38 - n(A∩B)  

n(A∩B) = 38 - 30  

n(A∩B) = 8

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

n(U) = 26 + 19

 n(U) = 45



4)  

 If n(A) = 25,n(B) = 10,n(AUB) = 20, n(A') = 13, Find n(A∩B) and n(U).

A
B
25
10
20
 

 n(A∩B) = Answer: 15

 n(U) = Answer: 38


SOLUTION 1 :

 n(A) = 25,

n(B) = 10,

n(AUB) = 20,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

20 = 25 + 10 - n(A∩B)  

20 = 35 - n(A∩B)  

n(A∩B) = 35 - 20  

n(A∩B) = 15

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

n(U) = 25 + 13

 n(U) = 38



5)  

 If n(A) = 16,n(B) = 15,n(AUB) = 26, n(A') = 11, Find n(A∩B) and n(U).

A
B
16
15
26
 

 n(A∩B) = Answer: 5

 n(U) = Answer: 27


SOLUTION 1 :

 n(A) = 16,

n(B) = 15,

n(AUB) = 26,

n(A") = 11

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

26 = 16 + 15 - n(A∩B)  

26 = 31 - n(A∩B)  

n(A∩B) = 31 - 26  

n(A∩B) = 5

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

n(U) = 16 + 11

 n(U) = 27



6)  

 If n(A) = 21,n(B) = 10,n(AUB) = 27, n(A') = 12, Find n(A∩B) and n(U).

A
B
21
10
27
 

 n(A∩B) = Answer: 4

 n(U) = Answer: 33


SOLUTION 1 :

 n(A) = 21,

n(B) = 10,

n(AUB) = 27,

n(A") = 12

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

27 = 21 + 10 - n(A∩B)  

27 = 31 - n(A∩B)  

n(A∩B) = 31 - 27  

n(A∩B) = 4

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

n(U) = 21 + 12

 n(U) = 33



7)  

 If n(A) = 22,n(B) = 13,n(AUB) = 29, n(A') = 10, Find n(A∩B) and n(U).

A
B
22
13
29
 

 n(A∩B) = Answer: 6

 n(U) = Answer: 32


SOLUTION 1 :

 n(A) = 22,

n(B) = 13,

n(AUB) = 29,

n(A") = 10

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

29 = 22 + 13 - n(A∩B)  

29 = 35 - n(A∩B)  

n(A∩B) = 35 - 29  

n(A∩B) = 6

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

n(U) = 22 + 10

 n(U) = 32



8)  

 If n(A) = 24,n(B) = 21,n(AUB) = 23, n(A') = 12, Find n(A∩B) and n(U).

A
B
24
21
23
 

 n(A∩B) = Answer: 22

 n(U) = Answer: 36


SOLUTION 1 :

 n(A) = 24,

n(B) = 21,

n(AUB) = 23,

n(A") = 12

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

23 = 24 + 21 - n(A∩B)  

23 = 45 - n(A∩B)  

n(A∩B) = 45 - 23  

n(A∩B) = 22

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

n(U) = 24 + 12

 n(U) = 36



9)  

 If n(A) = 21,n(B) = 13,n(AUB) = 29, n(A') = 14, Find n(A∩B) and n(U).

A
B
21
13
29
 

 n(A∩B) = Answer: 5

 n(U) = Answer: 35


SOLUTION 1 :

 n(A) = 21,

n(B) = 13,

n(AUB) = 29,

n(A") = 14

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

29 = 21 + 13 - n(A∩B)  

29 = 34 - n(A∩B)  

n(A∩B) = 34 - 29  

n(A∩B) = 5

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

n(U) = 21 + 14

 n(U) = 35



10)  

 If n(A) = 16,n(B) = 11,n(AUB) = 29, n(A') = 20, Find n(A∩B) and n(U).

A
B
16
11
29
 

 n(A∩B) = Answer: -2

 n(U) = Answer: 36


SOLUTION 1 :

 n(A) = 16,

n(B) = 11,

n(AUB) = 29,

n(A") = 20

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

29 = 16 + 11 - n(A∩B)  

29 = 27 - n(A∩B)  

n(A∩B) = 27 - 29  

n(A∩B) = -2

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

n(U) = 16 + 20

 n(U) = 36