Scroll:set and function >> Exercice 1.3 >> saq (4259)


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) = 988, n(A) = 309, n(B) = 366 and n(A∪B) = 449,

find n(A‘∪B‘).


Answer:_______________




2)  

 If A and B are two sets and U is the universal set such that n(U) = 781, n(A) = 337, n(B) = 333 and n(A∪B) = 495,

find n(A‘∪B‘).


Answer:_______________




3)  

 If A and B are two sets and U is the universal set such that n(U) = 851, n(A) = 304, n(B) = 442 and n(A∪B) = 481,

find n(A‘∪B‘).


Answer:_______________




4)  

 If A and B are two sets and U is the universal set such that n(U) = 871, n(A) = 340, n(B) = 445 and n(A∪B) = 459,

find n(A‘∪B‘).


Answer:_______________




5)  

 If A and B are two sets and U is the universal set such that n(U) = 920, n(A) = 385, n(B) = 425 and n(A∪B) = 473,

find n(A‘∪B‘).


Answer:_______________




6)  

 If A and B are two sets and U is the universal set such that n(U) = 922, n(A) = 331, n(B) = 315 and n(A∪B) = 405,

find n(A‘∪B‘).


Answer:_______________




7)  

 If A and B are two sets and U is the universal set such that n(U) = 854, n(A) = 389, n(B) = 379 and n(A∪B) = 428,

find n(A‘∪B‘).


Answer:_______________




8)  

 If A and B are two sets and U is the universal set such that n(U) = 806, n(A) = 310, n(B) = 498 and n(A∪B) = 469,

find n(A‘∪B‘).


Answer:_______________




9)  

 If A and B are two sets and U is the universal set such that n(U) = 881, n(A) = 367, n(B) = 463 and n(A∪B) = 458,

find n(A‘∪B‘).


Answer:_______________




10)  

 If A and B are two sets and U is the universal set such that n(U) = 724, n(A) = 362, n(B) = 478 and n(A∪B) = 450,

find n(A‘∪B‘).


Answer:_______________




 

1)  

 If A and B are two sets and U is the universal set such that n(U) = 988, n(A) = 309, n(B) = 366 and n(A∪B) = 449,

find n(A‘∪B‘).

Answer: 762


SOLUTION 1 :

 Given :

n(U) = 988

n(A) = 309

n(B) = 366

   n(A∪B) = 449,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 309 + 366 - 449

         = 675 - 449 = 226

∴ n(A∩B) = 226

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 988 - 226 = 762

   n(A‘∪B‘)  = 762



2)  

 If A and B are two sets and U is the universal set such that n(U) = 781, n(A) = 337, n(B) = 333 and n(A∪B) = 495,

find n(A‘∪B‘).

Answer: 606


SOLUTION 1 :

 Given :

n(U) = 781

n(A) = 337

n(B) = 333

   n(A∪B) = 495,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 337 + 333 - 495

         = 670 - 495 = 175

∴ n(A∩B) = 175

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 781 - 175 = 606

   n(A‘∪B‘)  = 606



3)  

 If A and B are two sets and U is the universal set such that n(U) = 851, n(A) = 304, n(B) = 442 and n(A∪B) = 481,

find n(A‘∪B‘).

Answer: 586


SOLUTION 1 :

 Given :

n(U) = 851

n(A) = 304

n(B) = 442

   n(A∪B) = 481,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 304 + 442 - 481

         = 746 - 481 = 265

∴ n(A∩B) = 265

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 851 - 265 = 586

   n(A‘∪B‘)  = 586



4)  

 If A and B are two sets and U is the universal set such that n(U) = 871, n(A) = 340, n(B) = 445 and n(A∪B) = 459,

find n(A‘∪B‘).

Answer: 545


SOLUTION 1 :

 Given :

n(U) = 871

n(A) = 340

n(B) = 445

   n(A∪B) = 459,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 340 + 445 - 459

         = 785 - 459 = 326

∴ n(A∩B) = 326

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 871 - 326 = 545

   n(A‘∪B‘)  = 545



5)  

 If A and B are two sets and U is the universal set such that n(U) = 920, n(A) = 385, n(B) = 425 and n(A∪B) = 473,

find n(A‘∪B‘).

Answer: 583


SOLUTION 1 :

 Given :

n(U) = 920

n(A) = 385

n(B) = 425

   n(A∪B) = 473,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 385 + 425 - 473

         = 810 - 473 = 337

∴ n(A∩B) = 337

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 920 - 337 = 583

   n(A‘∪B‘)  = 583



6)  

 If A and B are two sets and U is the universal set such that n(U) = 922, n(A) = 331, n(B) = 315 and n(A∪B) = 405,

find n(A‘∪B‘).

Answer: 681


SOLUTION 1 :

 Given :

n(U) = 922

n(A) = 331

n(B) = 315

   n(A∪B) = 405,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 331 + 315 - 405

         = 646 - 405 = 241

∴ n(A∩B) = 241

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 922 - 241 = 681

   n(A‘∪B‘)  = 681



7)  

 If A and B are two sets and U is the universal set such that n(U) = 854, n(A) = 389, n(B) = 379 and n(A∪B) = 428,

find n(A‘∪B‘).

Answer: 514


SOLUTION 1 :

 Given :

n(U) = 854

n(A) = 389

n(B) = 379

   n(A∪B) = 428,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 389 + 379 - 428

         = 768 - 428 = 340

∴ n(A∩B) = 340

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 854 - 340 = 514

   n(A‘∪B‘)  = 514



8)  

 If A and B are two sets and U is the universal set such that n(U) = 806, n(A) = 310, n(B) = 498 and n(A∪B) = 469,

find n(A‘∪B‘).

Answer: 467


SOLUTION 1 :

 Given :

n(U) = 806

n(A) = 310

n(B) = 498

   n(A∪B) = 469,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 310 + 498 - 469

         = 808 - 469 = 339

∴ n(A∩B) = 339

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 806 - 339 = 467

   n(A‘∪B‘)  = 467



9)  

 If A and B are two sets and U is the universal set such that n(U) = 881, n(A) = 367, n(B) = 463 and n(A∪B) = 458,

find n(A‘∪B‘).

Answer: 509


SOLUTION 1 :

 Given :

n(U) = 881

n(A) = 367

n(B) = 463

   n(A∪B) = 458,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 367 + 463 - 458

         = 830 - 458 = 372

∴ n(A∩B) = 372

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 881 - 372 = 509

   n(A‘∪B‘)  = 509



10)  

 If A and B are two sets and U is the universal set such that n(U) = 724, n(A) = 362, n(B) = 478 and n(A∪B) = 450,

find n(A‘∪B‘).

Answer: 334


SOLUTION 1 :

 Given :

n(U) = 724

n(A) = 362

n(B) = 478

   n(A∪B) = 450,

To find : n(A‘∪B‘).

we know that A‘∪B‘ = (A∩B)‘

Now, n(A∪B) = n(A) + n(B) - n(A∩B)

∴ n(A∩B) = n(A) + n(B) - n(A∪B)

          = 362 + 478 - 450

         = 840 - 450 = 390

∴ n(A∩B) = 390

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 724 - 390 = 334

   n(A‘∪B‘)  = 334