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) = 723, n(A) = 344, n(B) = 413 and n(A∪B) = 403,

find n(A‘∪B‘).


Answer:_______________




2)  

 If A and B are two sets and U is the universal set such that n(U) = 932, n(A) = 353, n(B) = 347 and n(A∪B) = 483,

find n(A‘∪B‘).


Answer:_______________




3)  

 If A and B are two sets and U is the universal set such that n(U) = 778, n(A) = 338, n(B) = 462 and n(A∪B) = 466,

find n(A‘∪B‘).


Answer:_______________




4)  

 If A and B are two sets and U is the universal set such that n(U) = 854, n(A) = 322, n(B) = 459 and n(A∪B) = 436,

find n(A‘∪B‘).


Answer:_______________




5)  

 If A and B are two sets and U is the universal set such that n(U) = 746, n(A) = 350, n(B) = 462 and n(A∪B) = 480,

find n(A‘∪B‘).


Answer:_______________




6)  

 If A and B are two sets and U is the universal set such that n(U) = 719, n(A) = 306, n(B) = 455 and n(A∪B) = 406,

find n(A‘∪B‘).


Answer:_______________




7)  

 If A and B are two sets and U is the universal set such that n(U) = 996, n(A) = 335, n(B) = 493 and n(A∪B) = 491,

find n(A‘∪B‘).


Answer:_______________




8)  

 If A and B are two sets and U is the universal set such that n(U) = 938, n(A) = 356, n(B) = 438 and n(A∪B) = 449,

find n(A‘∪B‘).


Answer:_______________




9)  

 If A and B are two sets and U is the universal set such that n(U) = 715, n(A) = 313, n(B) = 397 and n(A∪B) = 418,

find n(A‘∪B‘).


Answer:_______________




10)  

 If A and B are two sets and U is the universal set such that n(U) = 811, n(A) = 362, n(B) = 439 and n(A∪B) = 473,

find n(A‘∪B‘).


Answer:_______________




 

1)  

 If A and B are two sets and U is the universal set such that n(U) = 723, n(A) = 344, n(B) = 413 and n(A∪B) = 403,

find n(A‘∪B‘).

Answer: 369


SOLUTION 1 :

 Given :

n(U) = 723

n(A) = 344

n(B) = 413

   n(A∪B) = 403,

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)

          = 344 + 413 - 403

         = 757 - 403 = 354

∴ n(A∩B) = 354

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 723 - 354 = 369

   n(A‘∪B‘)  = 369



2)  

 If A and B are two sets and U is the universal set such that n(U) = 932, n(A) = 353, n(B) = 347 and n(A∪B) = 483,

find n(A‘∪B‘).

Answer: 715


SOLUTION 1 :

 Given :

n(U) = 932

n(A) = 353

n(B) = 347

   n(A∪B) = 483,

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)

          = 353 + 347 - 483

         = 700 - 483 = 217

∴ n(A∩B) = 217

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 932 - 217 = 715

   n(A‘∪B‘)  = 715



3)  

 If A and B are two sets and U is the universal set such that n(U) = 778, n(A) = 338, n(B) = 462 and n(A∪B) = 466,

find n(A‘∪B‘).

Answer: 444


SOLUTION 1 :

 Given :

n(U) = 778

n(A) = 338

n(B) = 462

   n(A∪B) = 466,

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)

          = 338 + 462 - 466

         = 800 - 466 = 334

∴ n(A∩B) = 334

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 778 - 334 = 444

   n(A‘∪B‘)  = 444



4)  

 If A and B are two sets and U is the universal set such that n(U) = 854, n(A) = 322, n(B) = 459 and n(A∪B) = 436,

find n(A‘∪B‘).

Answer: 509


SOLUTION 1 :

 Given :

n(U) = 854

n(A) = 322

n(B) = 459

   n(A∪B) = 436,

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)

          = 322 + 459 - 436

         = 781 - 436 = 345

∴ n(A∩B) = 345

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 854 - 345 = 509

   n(A‘∪B‘)  = 509



5)  

 If A and B are two sets and U is the universal set such that n(U) = 746, n(A) = 350, n(B) = 462 and n(A∪B) = 480,

find n(A‘∪B‘).

Answer: 414


SOLUTION 1 :

 Given :

n(U) = 746

n(A) = 350

n(B) = 462

   n(A∪B) = 480,

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)

          = 350 + 462 - 480

         = 812 - 480 = 332

∴ n(A∩B) = 332

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 746 - 332 = 414

   n(A‘∪B‘)  = 414



6)  

 If A and B are two sets and U is the universal set such that n(U) = 719, n(A) = 306, n(B) = 455 and n(A∪B) = 406,

find n(A‘∪B‘).

Answer: 364


SOLUTION 1 :

 Given :

n(U) = 719

n(A) = 306

n(B) = 455

   n(A∪B) = 406,

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)

          = 306 + 455 - 406

         = 761 - 406 = 355

∴ n(A∩B) = 355

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 719 - 355 = 364

   n(A‘∪B‘)  = 364



7)  

 If A and B are two sets and U is the universal set such that n(U) = 996, n(A) = 335, n(B) = 493 and n(A∪B) = 491,

find n(A‘∪B‘).

Answer: 659


SOLUTION 1 :

 Given :

n(U) = 996

n(A) = 335

n(B) = 493

   n(A∪B) = 491,

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)

          = 335 + 493 - 491

         = 828 - 491 = 337

∴ n(A∩B) = 337

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 996 - 337 = 659

   n(A‘∪B‘)  = 659



8)  

 If A and B are two sets and U is the universal set such that n(U) = 938, n(A) = 356, n(B) = 438 and n(A∪B) = 449,

find n(A‘∪B‘).

Answer: 593


SOLUTION 1 :

 Given :

n(U) = 938

n(A) = 356

n(B) = 438

   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)

          = 356 + 438 - 449

         = 794 - 449 = 345

∴ n(A∩B) = 345

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 938 - 345 = 593

   n(A‘∪B‘)  = 593



9)  

 If A and B are two sets and U is the universal set such that n(U) = 715, n(A) = 313, n(B) = 397 and n(A∪B) = 418,

find n(A‘∪B‘).

Answer: 423


SOLUTION 1 :

 Given :

n(U) = 715

n(A) = 313

n(B) = 397

   n(A∪B) = 418,

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)

          = 313 + 397 - 418

         = 710 - 418 = 292

∴ n(A∩B) = 292

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 715 - 292 = 423

   n(A‘∪B‘)  = 423



10)  

 If A and B are two sets and U is the universal set such that n(U) = 811, n(A) = 362, n(B) = 439 and n(A∪B) = 473,

find n(A‘∪B‘).

Answer: 483


SOLUTION 1 :

 Given :

n(U) = 811

n(A) = 362

n(B) = 439

   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)

          = 362 + 439 - 473

         = 801 - 473 = 328

∴ n(A∩B) = 328

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 811 - 328 = 483

   n(A‘∪B‘)  = 483