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) = 22,n(B) = 14,n(AUB) = 29, n(A') = 11, Find n(A∩B) and n(U).

A
B
22
14
29
 

 n(A∩B) =

 n(U) =



Answer:_______________




2)  

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

A
B
22
18
30
 

 n(A∩B) =

 n(U) =



Answer:_______________




3)  

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

A
B
16
18
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




4)  

 If n(A) = 17,n(B) = 21,n(AUB) = 22, n(A') = 10, Find n(A∩B) and n(U).

A
B
17
21
22
 

 n(A∩B) =

 n(U) =



Answer:_______________




5)  

 If n(A) = 26,n(B) = 16,n(AUB) = 26, n(A') = 20, Find n(A∩B) and n(U).

A
B
26
16
26
 

 n(A∩B) =

 n(U) =



Answer:_______________




6)  

 If n(A) = 24,n(B) = 24,n(AUB) = 29, n(A') = 13, Find n(A∩B) and n(U).

A
B
24
24
29
 

 n(A∩B) =

 n(U) =



Answer:_______________




7)  

 If n(A) = 25,n(B) = 12,n(AUB) = 30, n(A') = 11, Find n(A∩B) and n(U).

A
B
25
12
30
 

 n(A∩B) =

 n(U) =



Answer:_______________




8)  

 If n(A) = 15,n(B) = 25,n(AUB) = 21, n(A') = 17, Find n(A∩B) and n(U).

A
B
15
25
21
 

 n(A∩B) =

 n(U) =



Answer:_______________




9)  

 If n(A) = 23,n(B) = 12,n(AUB) = 24, n(A') = 17, Find n(A∩B) and n(U).

A
B
23
12
24
 

 n(A∩B) =

 n(U) =



Answer:_______________




10)  

 If n(A) = 16,n(B) = 15,n(AUB) = 28, n(A') = 14, Find n(A∩B) and n(U).

A
B
16
15
28
 

 n(A∩B) =

 n(U) =



Answer:_______________




 

1)  

 If n(A) = 22,n(B) = 14,n(AUB) = 29, n(A') = 11, Find n(A∩B) and n(U).

A
B
22
14
29
 

 n(A∩B) = Answer: 7

 n(U) = Answer: 33


SOLUTION 1 :

 n(A) = 22,

n(B) = 14,

n(AUB) = 29,

n(A") = 11

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

29 = 22 + 14 - n(A∩B)  

29 = 36 - n(A∩B)  

n(A∩B) = 36 - 29  

n(A∩B) = 7

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

n(U) = 22 + 11

 n(U) = 33



2)  

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

A
B
22
18
30
 

 n(A∩B) = Answer: 10

 n(U) = Answer: 41


SOLUTION 1 :

 n(A) = 22,

n(B) = 18,

n(AUB) = 30,

n(A") = 19

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

30 = 22 + 18 - n(A∩B)  

30 = 40 - n(A∩B)  

n(A∩B) = 40 - 30  

n(A∩B) = 10

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

n(U) = 22 + 19

 n(U) = 41



3)  

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

A
B
16
18
28
 

 n(A∩B) = Answer: 6

 n(U) = Answer: 32


SOLUTION 1 :

 n(A) = 16,

n(B) = 18,

n(AUB) = 28,

n(A") = 16

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 16 + 18 - n(A∩B)  

28 = 34 - n(A∩B)  

n(A∩B) = 34 - 28  

n(A∩B) = 6

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

n(U) = 16 + 16

 n(U) = 32



4)  

 If n(A) = 17,n(B) = 21,n(AUB) = 22, n(A') = 10, Find n(A∩B) and n(U).

A
B
17
21
22
 

 n(A∩B) = Answer: 16

 n(U) = Answer: 27


SOLUTION 1 :

 n(A) = 17,

n(B) = 21,

n(AUB) = 22,

n(A") = 10

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

22 = 17 + 21 - n(A∩B)  

22 = 38 - n(A∩B)  

n(A∩B) = 38 - 22  

n(A∩B) = 16

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

n(U) = 17 + 10

 n(U) = 27



5)  

 If n(A) = 26,n(B) = 16,n(AUB) = 26, n(A') = 20, Find n(A∩B) and n(U).

A
B
26
16
26
 

 n(A∩B) = Answer: 16

 n(U) = Answer: 46


SOLUTION 1 :

 n(A) = 26,

n(B) = 16,

n(AUB) = 26,

n(A") = 20

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

26 = 26 + 16 - n(A∩B)  

26 = 42 - n(A∩B)  

n(A∩B) = 42 - 26  

n(A∩B) = 16

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

n(U) = 26 + 20

 n(U) = 46



6)  

 If n(A) = 24,n(B) = 24,n(AUB) = 29, n(A') = 13, Find n(A∩B) and n(U).

A
B
24
24
29
 

 n(A∩B) = Answer: 19

 n(U) = Answer: 37


SOLUTION 1 :

 n(A) = 24,

n(B) = 24,

n(AUB) = 29,

n(A") = 13

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

29 = 24 + 24 - n(A∩B)  

29 = 48 - n(A∩B)  

n(A∩B) = 48 - 29  

n(A∩B) = 19

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

n(U) = 24 + 13

 n(U) = 37



7)  

 If n(A) = 25,n(B) = 12,n(AUB) = 30, n(A') = 11, Find n(A∩B) and n(U).

A
B
25
12
30
 

 n(A∩B) = Answer: 7

 n(U) = Answer: 36


SOLUTION 1 :

 n(A) = 25,

n(B) = 12,

n(AUB) = 30,

n(A") = 11

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

30 = 25 + 12 - n(A∩B)  

30 = 37 - n(A∩B)  

n(A∩B) = 37 - 30  

n(A∩B) = 7

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

n(U) = 25 + 11

 n(U) = 36



8)  

 If n(A) = 15,n(B) = 25,n(AUB) = 21, n(A') = 17, Find n(A∩B) and n(U).

A
B
15
25
21
 

 n(A∩B) = Answer: 19

 n(U) = Answer: 32


SOLUTION 1 :

 n(A) = 15,

n(B) = 25,

n(AUB) = 21,

n(A") = 17

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

21 = 15 + 25 - n(A∩B)  

21 = 40 - n(A∩B)  

n(A∩B) = 40 - 21  

n(A∩B) = 19

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

n(U) = 15 + 17

 n(U) = 32



9)  

 If n(A) = 23,n(B) = 12,n(AUB) = 24, n(A') = 17, Find n(A∩B) and n(U).

A
B
23
12
24
 

 n(A∩B) = Answer: 11

 n(U) = Answer: 40


SOLUTION 1 :

 n(A) = 23,

n(B) = 12,

n(AUB) = 24,

n(A") = 17

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

24 = 23 + 12 - 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) = 23 + 17

 n(U) = 40



10)  

 If n(A) = 16,n(B) = 15,n(AUB) = 28, n(A') = 14, Find n(A∩B) and n(U).

A
B
16
15
28
 

 n(A∩B) = Answer: 3

 n(U) = Answer: 30


SOLUTION 1 :

 n(A) = 16,

n(B) = 15,

n(AUB) = 28,

n(A") = 14

n(A∩B) = 

 n(AUB) =  n(A) + n(B) - n(A∩B)  

28 = 16 + 15 - n(A∩B)  

28 = 31 - n(A∩B)  

n(A∩B) = 31 - 28  

n(A∩B) = 3

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

n(U) = 16 + 14

 n(U) = 30