Scroll:set and function >> Exercice 1.3 >> saq (4258)


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 A and B are two sets and U is the universal set such that n(U) = 1644, n(A) = 387, n(B) = 540 and n(A∩B) = 114,

find n(A‘∩B‘).



Answer:_______________




2)  

 If A and B are two sets and U is the universal set such that n(U) = 1400, n(A) = 350, n(B) = 600 and n(A∩B) = 100,

find n(A‘∩B‘).

  

 


Answer:_______________




3)  

 If A and B are two sets and U is the universal set such that n(U) = 1190, n(A) = 360, n(B) = 570 and n(A∩B) = 170,

find n(A‘∩B‘).

  

 


Answer:_______________




4)  

 If A and B are two sets and U is the universal set such that n(U) = 1607, n(A) = 370, n(B) = 502 and n(A∩B) = 116,

find n(A‘∩B‘).



Answer:_______________




5)  

 If A and B are two sets and U is the universal set such that n(U) = 1800, n(A) = 300, n(B) = 650 and n(A∩B) = 100,

find n(A‘∩B‘).

  

 


Answer:_______________




6)  

 If A and B are two sets and U is the universal set such that n(U) = 1670, n(A) = 330, n(B) = 690 and n(A∩B) = 100,

find n(A‘∩B‘).

  

 


Answer:_______________




7)  

 If A and B are two sets and U is the universal set such that n(U) = 1364, n(A) = 367, n(B) = 506 and n(A∩B) = 162,

find n(A‘∩B‘).



Answer:_______________




8)  

 If A and B are two sets and U is the universal set such that n(U) = 1300, n(A) = 350, n(B) = 600 and n(A∩B) = 100,

find n(A‘∩B‘).

  

 


Answer:_______________




9)  

 If A and B are two sets and U is the universal set such that n(U) = 1440, n(A) = 330, n(B) = 680 and n(A∩B) = 170,

find n(A‘∩B‘).

  

 


Answer:_______________




10)  

 If A and B are two sets and U is the universal set such that n(U) = 1198, n(A) = 343, n(B) = 516 and n(A∩B) = 156,

find n(A‘∩B‘).



Answer:_______________




 

1)  

 If A and B are two sets and U is the universal set such that n(U) = 1644, n(A) = 387, n(B) = 540 and n(A∩B) = 114,

find n(A‘∩B‘).

Answer: 831


SOLUTION 1 :

 Given :

n(U) = 1644

n(A) = 387

n(B) = 540

   n(A∩B) = 114,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 387 + 540 - 114

         = 927 - 114 = 813

∴ n(A∪B) = 813

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1644 - 813 = 831

   n(A‘∩B‘)  = 831



2)  

 If A and B are two sets and U is the universal set such that n(U) = 1400, n(A) = 350, n(B) = 600 and n(A∩B) = 100,

find n(A‘∩B‘).

Answer: 550

  

 


SOLUTION 1 :

 Given :

n(U) = 1400

n(A) = 350

n(B) = 600

   n(A∩B) = 100,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 350 + 600 - 100

         = 950 - 100 = 850

∴ n(A∪B) = 850

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1400 - 850 = 550

   n(A‘∩B‘)  = 550



3)  

 If A and B are two sets and U is the universal set such that n(U) = 1190, n(A) = 360, n(B) = 570 and n(A∩B) = 170,

find n(A‘∩B‘).

Answer: 430

  

 


SOLUTION 1 :

 Given :

n(U) = 1190

n(A) = 360

n(B) = 570

   n(A∩B) = 170,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 360 + 570 - 170

         = 930 - 170 = 760

∴ n(A∪B) = 760

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1190 - 760 = 430

   n(A‘∩B‘)  = 430



4)  

 If A and B are two sets and U is the universal set such that n(U) = 1607, n(A) = 370, n(B) = 502 and n(A∩B) = 116,

find n(A‘∩B‘).

Answer: 851


SOLUTION 1 :

 Given :

n(U) = 1607

n(A) = 370

n(B) = 502

   n(A∩B) = 116,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 370 + 502 - 116

         = 872 - 116 = 756

∴ n(A∪B) = 756

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1607 - 756 = 851

   n(A‘∩B‘)  = 851



5)  

 If A and B are two sets and U is the universal set such that n(U) = 1800, n(A) = 300, n(B) = 650 and n(A∩B) = 100,

find n(A‘∩B‘).

Answer: 950

  

 


SOLUTION 1 :

 Given :

n(U) = 1800

n(A) = 300

n(B) = 650

   n(A∩B) = 100,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 300 + 650 - 100

         = 950 - 100 = 850

∴ n(A∪B) = 850

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1800 - 850 = 950

   n(A‘∩B‘)  = 950



6)  

 If A and B are two sets and U is the universal set such that n(U) = 1670, n(A) = 330, n(B) = 690 and n(A∩B) = 100,

find n(A‘∩B‘).

Answer: 750

  

 


SOLUTION 1 :

 Given :

n(U) = 1670

n(A) = 330

n(B) = 690

   n(A∩B) = 100,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 330 + 690 - 100

         = 1020 - 100 = 920

∴ n(A∪B) = 920

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1670 - 920 = 750

   n(A‘∩B‘)  = 750



7)  

 If A and B are two sets and U is the universal set such that n(U) = 1364, n(A) = 367, n(B) = 506 and n(A∩B) = 162,

find n(A‘∩B‘).

Answer: 653


SOLUTION 1 :

 Given :

n(U) = 1364

n(A) = 367

n(B) = 506

   n(A∩B) = 162,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 367 + 506 - 162

         = 873 - 162 = 711

∴ n(A∪B) = 711

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1364 - 711 = 653

   n(A‘∩B‘)  = 653



8)  

 If A and B are two sets and U is the universal set such that n(U) = 1300, n(A) = 350, n(B) = 600 and n(A∩B) = 100,

find n(A‘∩B‘).

Answer: 450

  

 


SOLUTION 1 :

 Given :

n(U) = 1300

n(A) = 350

n(B) = 600

   n(A∩B) = 100,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 350 + 600 - 100

         = 950 - 100 = 850

∴ n(A∪B) = 850

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1300 - 850 = 450

   n(A‘∩B‘)  = 450



9)  

 If A and B are two sets and U is the universal set such that n(U) = 1440, n(A) = 330, n(B) = 680 and n(A∩B) = 170,

find n(A‘∩B‘).

Answer: 600

  

 


SOLUTION 1 :

 Given :

n(U) = 1440

n(A) = 330

n(B) = 680

   n(A∩B) = 170,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 330 + 680 - 170

         = 1010 - 170 = 840

∴ n(A∪B) = 840

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1440 - 840 = 600

   n(A‘∩B‘)  = 600



10)  

 If A and B are two sets and U is the universal set such that n(U) = 1198, n(A) = 343, n(B) = 516 and n(A∩B) = 156,

find n(A‘∩B‘).

Answer: 495


SOLUTION 1 :

 Given :

n(U) = 1198

n(A) = 343

n(B) = 516

   n(A∩B) = 156,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 343 + 516 - 156

         = 859 - 156 = 703

∴ n(A∪B) = 703

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1198 - 703 = 495

   n(A‘∩B‘)  = 495