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) = 1514, n(A) = 300, n(B) = 543 and n(A∩B) = 148,

find n(A‘∩B‘).



Answer:_______________




2)  

 If A and B are two sets and U is the universal set such that n(U) = 1300, n(A) = 320, n(B) = 500 and n(A∩B) = 110,

find n(A‘∩B‘).

  

 


Answer:_______________




3)  

 If A and B are two sets and U is the universal set such that n(U) = 1700, n(A) = 350, n(B) = 550 and n(A∩B) = 100,

find n(A‘∩B‘).

  

 


Answer:_______________




4)  

 If A and B are two sets and U is the universal set such that n(U) = 1620, n(A) = 382, n(B) = 515 and n(A∩B) = 123,

find n(A‘∩B‘).



Answer:_______________




5)  

 If A and B are two sets and U is the universal set such that n(U) = 1050, n(A) = 360, n(B) = 600 and n(A∩B) = 160,

find n(A‘∩B‘).

  

 


Answer:_______________




6)  

 If A and B are two sets and U is the universal set such that n(U) = 1000, n(A) = 300, n(B) = 500 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) = 1644, n(A) = 383, n(B) = 598 and n(A∩B) = 182,

find n(A‘∩B‘).



Answer:_______________




8)  

 If A and B are two sets and U is the universal set such that n(U) = 1830, n(A) = 340, n(B) = 540 and n(A∩B) = 160,

find n(A‘∩B‘).

  

 


Answer:_______________




9)  

 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) = 150,

find n(A‘∩B‘).

  

 


Answer:_______________




10)  

 If A and B are two sets and U is the universal set such that n(U) = 1538, n(A) = 303, n(B) = 587 and n(A∩B) = 116,

find n(A‘∩B‘).



Answer:_______________




 

1)  

 If A and B are two sets and U is the universal set such that n(U) = 1514, n(A) = 300, n(B) = 543 and n(A∩B) = 148,

find n(A‘∩B‘).

Answer: 819


SOLUTION 1 :

 Given :

n(U) = 1514

n(A) = 300

n(B) = 543

   n(A∩B) = 148,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 300 + 543 - 148

         = 843 - 148 = 695

∴ n(A∪B) = 695

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1514 - 695 = 819

   n(A‘∩B‘)  = 819



2)  

 If A and B are two sets and U is the universal set such that n(U) = 1300, n(A) = 320, n(B) = 500 and n(A∩B) = 110,

find n(A‘∩B‘).

Answer: 590

  

 


SOLUTION 1 :

 Given :

n(U) = 1300

n(A) = 320

n(B) = 500

   n(A∩B) = 110,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 320 + 500 - 110

         = 820 - 110 = 710

∴ n(A∪B) = 710

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1300 - 710 = 590

   n(A‘∩B‘)  = 590



3)  

 If A and B are two sets and U is the universal set such that n(U) = 1700, n(A) = 350, n(B) = 550 and n(A∩B) = 100,

find n(A‘∩B‘).

Answer: 900

  

 


SOLUTION 1 :

 Given :

n(U) = 1700

n(A) = 350

n(B) = 550

   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 + 550 - 100

         = 900 - 100 = 800

∴ n(A∪B) = 800

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1700 - 800 = 900

   n(A‘∩B‘)  = 900



4)  

 If A and B are two sets and U is the universal set such that n(U) = 1620, n(A) = 382, n(B) = 515 and n(A∩B) = 123,

find n(A‘∩B‘).

Answer: 846


SOLUTION 1 :

 Given :

n(U) = 1620

n(A) = 382

n(B) = 515

   n(A∩B) = 123,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 382 + 515 - 123

         = 897 - 123 = 774

∴ n(A∪B) = 774

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1620 - 774 = 846

   n(A‘∩B‘)  = 846



5)  

 If A and B are two sets and U is the universal set such that n(U) = 1050, n(A) = 360, n(B) = 600 and n(A∩B) = 160,

find n(A‘∩B‘).

Answer: 250

  

 


SOLUTION 1 :

 Given :

n(U) = 1050

n(A) = 360

n(B) = 600

   n(A∩B) = 160,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 360 + 600 - 160

         = 960 - 160 = 800

∴ n(A∪B) = 800

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1050 - 800 = 250

   n(A‘∩B‘)  = 250



6)  

 If A and B are two sets and U is the universal set such that n(U) = 1000, n(A) = 300, n(B) = 500 and n(A∩B) = 100,

find n(A‘∩B‘).

Answer: 300

  

 


SOLUTION 1 :

 Given :

n(U) = 1000

n(A) = 300

n(B) = 500

   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 + 500 - 100

         = 800 - 100 = 700

∴ n(A∪B) = 700

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1000 - 700 = 300

   n(A‘∩B‘)  = 300



7)  

 If A and B are two sets and U is the universal set such that n(U) = 1644, n(A) = 383, n(B) = 598 and n(A∩B) = 182,

find n(A‘∩B‘).

Answer: 845


SOLUTION 1 :

 Given :

n(U) = 1644

n(A) = 383

n(B) = 598

   n(A∩B) = 182,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 383 + 598 - 182

         = 981 - 182 = 799

∴ n(A∪B) = 799

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1644 - 799 = 845

   n(A‘∩B‘)  = 845



8)  

 If A and B are two sets and U is the universal set such that n(U) = 1830, n(A) = 340, n(B) = 540 and n(A∩B) = 160,

find n(A‘∩B‘).

Answer: 1110

  

 


SOLUTION 1 :

 Given :

n(U) = 1830

n(A) = 340

n(B) = 540

   n(A∩B) = 160,

To find : n(A‘∩B‘).

we know that A‘∩B‘ = (A∪B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

          = 340 + 540 - 160

         = 880 - 160 = 720

∴ n(A∪B) = 720

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1830 - 720 = 1110

   n(A‘∩B‘)  = 1110



9)  

 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) = 150,

find n(A‘∩B‘).

Answer: 600

  

 


SOLUTION 1 :

 Given :

n(U) = 1400

n(A) = 350

n(B) = 600

   n(A∩B) = 150,

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 - 150

         = 950 - 150 = 800

∴ n(A∪B) = 800

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1400 - 800 = 600

   n(A‘∩B‘)  = 600



10)  

 If A and B are two sets and U is the universal set such that n(U) = 1538, n(A) = 303, n(B) = 587 and n(A∩B) = 116,

find n(A‘∩B‘).

Answer: 764


SOLUTION 1 :

 Given :

n(U) = 1538

n(A) = 303

n(B) = 587

   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)

          = 303 + 587 - 116

         = 890 - 116 = 774

∴ n(A∪B) = 774

 n(A‘B‘) = n[(A∪B)‘]

 n(A‘∩B‘) = n[(A∪B)‘] = n(U) - n(A∪B)

    = 1538 - 774 = 764

   n(A‘∩B‘)  = 764