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) = 20,n(B) = 19,n(AUB) = 26, n(A') = 12, Find n(A∩B) and n(U).

A
B
20
19
26
 

 n(A∩B) =

 n(U) =



Answer:_______________




2)  

 If n(A) = 22,n(B) = 16,n(AUB) = 28, n(A') = 18, Find n(A∩B) and n(U).

A
B
22
16
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




3)  

 If n(A) = 23,n(B) = 10,n(AUB) = 22, n(A') = 13, Find n(A∩B) and n(U).

A
B
23
10
22
 

 n(A∩B) =

 n(U) =



Answer:_______________




4)  

 If n(A) = 22,n(B) = 25,n(AUB) = 28, n(A') = 18, Find n(A∩B) and n(U).

A
B
22
25
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




5)  

 If n(A) = 23,n(B) = 12,n(AUB) = 25, n(A') = 13, Find n(A∩B) and n(U).

A
B
23
12
25
 

 n(A∩B) =

 n(U) =



Answer:_______________




6)  

 If n(A) = 23,n(B) = 19,n(AUB) = 28, n(A') = 19, Find n(A∩B) and n(U).

A
B
23
19
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




7)  

 If n(A) = 24,n(B) = 14,n(AUB) = 30, n(A') = 19, Find n(A∩B) and n(U).

A
B
24
14
30
 

 n(A∩B) =

 n(U) =



Answer:_______________




8)  

 If n(A) = 19,n(B) = 12,n(AUB) = 29, n(A') = 17, Find n(A∩B) and n(U).

A
B
19
12
29
 

 n(A∩B) =

 n(U) =



Answer:_______________




9)  

 If n(A) = 18,n(B) = 15,n(AUB) = 30, n(A') = 19, Find n(A∩B) and n(U).

A
B
18
15
30
 

 n(A∩B) =

 n(U) =



Answer:_______________




10)  

 If n(A) = 25,n(B) = 24,n(AUB) = 26, n(A') = 13, Find n(A∩B) and n(U).

A
B
25
24
26
 

 n(A∩B) =

 n(U) =



Answer:_______________




 

1)  

 If n(A) = 20,n(B) = 19,n(AUB) = 26, n(A') = 12, Find n(A∩B) and n(U).

A
B
20
19
26
 

 n(A∩B) = Answer: 13

 n(U) = Answer: 32


SOLUTION 1 :

 n(A) = 20,

n(B) = 19,

n(AUB) = 26,

n(A") = 12

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

26 = 20 + 19 - n(A∩B)  

26 = 39 - n(A∩B)  

n(A∩B) = 39 - 26  

n(A∩B) = 13

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

n(U) = 20 + 12

 n(U) = 32



2)  

 If n(A) = 22,n(B) = 16,n(AUB) = 28, n(A') = 18, Find n(A∩B) and n(U).

A
B
22
16
28
 

 n(A∩B) = Answer: 10

 n(U) = Answer: 40


SOLUTION 1 :

 n(A) = 22,

n(B) = 16,

n(AUB) = 28,

n(A") = 18

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 22 + 16 - n(A∩B)  

28 = 38 - n(A∩B)  

n(A∩B) = 38 - 28  

n(A∩B) = 10

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

n(U) = 22 + 18

 n(U) = 40



3)  

 If n(A) = 23,n(B) = 10,n(AUB) = 22, n(A') = 13, Find n(A∩B) and n(U).

A
B
23
10
22
 

 n(A∩B) = Answer: 11

 n(U) = Answer: 36


SOLUTION 1 :

 n(A) = 23,

n(B) = 10,

n(AUB) = 22,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

22 = 23 + 10 - n(A∩B)  

22 = 33 - n(A∩B)  

n(A∩B) = 33 - 22  

n(A∩B) = 11

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

n(U) = 23 + 13

 n(U) = 36



4)  

 If n(A) = 22,n(B) = 25,n(AUB) = 28, n(A') = 18, Find n(A∩B) and n(U).

A
B
22
25
28
 

 n(A∩B) = Answer: 19

 n(U) = Answer: 40


SOLUTION 1 :

 n(A) = 22,

n(B) = 25,

n(AUB) = 28,

n(A") = 18

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 22 + 25 - n(A∩B)  

28 = 47 - n(A∩B)  

n(A∩B) = 47 - 28  

n(A∩B) = 19

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

n(U) = 22 + 18

 n(U) = 40



5)  

 If n(A) = 23,n(B) = 12,n(AUB) = 25, n(A') = 13, Find n(A∩B) and n(U).

A
B
23
12
25
 

 n(A∩B) = Answer: 10

 n(U) = Answer: 36


SOLUTION 1 :

 n(A) = 23,

n(B) = 12,

n(AUB) = 25,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

25 = 23 + 12 - n(A∩B)  

25 = 35 - n(A∩B)  

n(A∩B) = 35 - 25  

n(A∩B) = 10

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

n(U) = 23 + 13

 n(U) = 36



6)  

 If n(A) = 23,n(B) = 19,n(AUB) = 28, n(A') = 19, Find n(A∩B) and n(U).

A
B
23
19
28
 

 n(A∩B) = Answer: 14

 n(U) = Answer: 42


SOLUTION 1 :

 n(A) = 23,

n(B) = 19,

n(AUB) = 28,

n(A") = 19

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 23 + 19 - 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) = 23 + 19

 n(U) = 42



7)  

 If n(A) = 24,n(B) = 14,n(AUB) = 30, n(A') = 19, Find n(A∩B) and n(U).

A
B
24
14
30
 

 n(A∩B) = Answer: 8

 n(U) = Answer: 43


SOLUTION 1 :

 n(A) = 24,

n(B) = 14,

n(AUB) = 30,

n(A") = 19

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

30 = 24 + 14 - 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) = 24 + 19

 n(U) = 43



8)  

 If n(A) = 19,n(B) = 12,n(AUB) = 29, n(A') = 17, Find n(A∩B) and n(U).

A
B
19
12
29
 

 n(A∩B) = Answer: 2

 n(U) = Answer: 36


SOLUTION 1 :

 n(A) = 19,

n(B) = 12,

n(AUB) = 29,

n(A") = 17

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

29 = 19 + 12 - n(A∩B)  

29 = 31 - n(A∩B)  

n(A∩B) = 31 - 29  

n(A∩B) = 2

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

n(U) = 19 + 17

 n(U) = 36



9)  

 If n(A) = 18,n(B) = 15,n(AUB) = 30, n(A') = 19, Find n(A∩B) and n(U).

A
B
18
15
30
 

 n(A∩B) = Answer: 3

 n(U) = Answer: 37


SOLUTION 1 :

 n(A) = 18,

n(B) = 15,

n(AUB) = 30,

n(A") = 19

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

30 = 18 + 15 - n(A∩B)  

30 = 33 - n(A∩B)  

n(A∩B) = 33 - 30  

n(A∩B) = 3

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

n(U) = 18 + 19

 n(U) = 37



10)  

 If n(A) = 25,n(B) = 24,n(AUB) = 26, n(A') = 13, Find n(A∩B) and n(U).

A
B
25
24
26
 

 n(A∩B) = Answer: 23

 n(U) = Answer: 38


SOLUTION 1 :

 n(A) = 25,

n(B) = 24,

n(AUB) = 26,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

26 = 25 + 24 - n(A∩B)  

26 = 49 - n(A∩B)  

n(A∩B) = 49 - 26  

n(A∩B) = 23

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

n(U) = 25 + 13

 n(U) = 38