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) = 792, n(A) = 371, n(B) = 491 and n(A∪B) = 494,

find n(A‘∪B‘).


Answer:_______________




2)  

 If A and B are two sets and U is the universal set such that n(U) = 878, n(A) = 342, n(B) = 326 and n(A∪B) = 490,

find n(A‘∪B‘).


Answer:_______________




3)  

 If A and B are two sets and U is the universal set such that n(U) = 961, n(A) = 312, n(B) = 462 and n(A∪B) = 429,

find n(A‘∪B‘).


Answer:_______________




4)  

 If A and B are two sets and U is the universal set such that n(U) = 937, n(A) = 324, n(B) = 301 and n(A∪B) = 442,

find n(A‘∪B‘).


Answer:_______________




5)  

 If A and B are two sets and U is the universal set such that n(U) = 719, n(A) = 305, n(B) = 484 and n(A∪B) = 430,

find n(A‘∪B‘).


Answer:_______________




6)  

 If A and B are two sets and U is the universal set such that n(U) = 829, n(A) = 353, n(B) = 303 and n(A∪B) = 409,

find n(A‘∪B‘).


Answer:_______________




7)  

 If A and B are two sets and U is the universal set such that n(U) = 956, n(A) = 368, n(B) = 337 and n(A∪B) = 440,

find n(A‘∪B‘).


Answer:_______________




8)  

 If A and B are two sets and U is the universal set such that n(U) = 886, n(A) = 368, n(B) = 334 and n(A∪B) = 499,

find n(A‘∪B‘).


Answer:_______________




9)  

 If A and B are two sets and U is the universal set such that n(U) = 852, n(A) = 351, n(B) = 447 and n(A∪B) = 416,

find n(A‘∪B‘).


Answer:_______________




10)  

 If A and B are two sets and U is the universal set such that n(U) = 929, n(A) = 307, n(B) = 452 and n(A∪B) = 451,

find n(A‘∪B‘).


Answer:_______________




 

1)  

 If A and B are two sets and U is the universal set such that n(U) = 792, n(A) = 371, n(B) = 491 and n(A∪B) = 494,

find n(A‘∪B‘).

Answer: 424


SOLUTION 1 :

 Given :

n(U) = 792

n(A) = 371

n(B) = 491

   n(A∪B) = 494,

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)

          = 371 + 491 - 494

         = 862 - 494 = 368

∴ n(A∩B) = 368

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 792 - 368 = 424

   n(A‘∪B‘)  = 424



2)  

 If A and B are two sets and U is the universal set such that n(U) = 878, n(A) = 342, n(B) = 326 and n(A∪B) = 490,

find n(A‘∪B‘).

Answer: 700


SOLUTION 1 :

 Given :

n(U) = 878

n(A) = 342

n(B) = 326

   n(A∪B) = 490,

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)

          = 342 + 326 - 490

         = 668 - 490 = 178

∴ n(A∩B) = 178

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 878 - 178 = 700

   n(A‘∪B‘)  = 700



3)  

 If A and B are two sets and U is the universal set such that n(U) = 961, n(A) = 312, n(B) = 462 and n(A∪B) = 429,

find n(A‘∪B‘).

Answer: 616


SOLUTION 1 :

 Given :

n(U) = 961

n(A) = 312

n(B) = 462

   n(A∪B) = 429,

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)

          = 312 + 462 - 429

         = 774 - 429 = 345

∴ n(A∩B) = 345

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 961 - 345 = 616

   n(A‘∪B‘)  = 616



4)  

 If A and B are two sets and U is the universal set such that n(U) = 937, n(A) = 324, n(B) = 301 and n(A∪B) = 442,

find n(A‘∪B‘).

Answer: 754


SOLUTION 1 :

 Given :

n(U) = 937

n(A) = 324

n(B) = 301

   n(A∪B) = 442,

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)

          = 324 + 301 - 442

         = 625 - 442 = 183

∴ n(A∩B) = 183

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 937 - 183 = 754

   n(A‘∪B‘)  = 754



5)  

 If A and B are two sets and U is the universal set such that n(U) = 719, n(A) = 305, n(B) = 484 and n(A∪B) = 430,

find n(A‘∪B‘).

Answer: 360


SOLUTION 1 :

 Given :

n(U) = 719

n(A) = 305

n(B) = 484

   n(A∪B) = 430,

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)

          = 305 + 484 - 430

         = 789 - 430 = 359

∴ n(A∩B) = 359

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 719 - 359 = 360

   n(A‘∪B‘)  = 360



6)  

 If A and B are two sets and U is the universal set such that n(U) = 829, n(A) = 353, n(B) = 303 and n(A∪B) = 409,

find n(A‘∪B‘).

Answer: 582


SOLUTION 1 :

 Given :

n(U) = 829

n(A) = 353

n(B) = 303

   n(A∪B) = 409,

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 + 303 - 409

         = 656 - 409 = 247

∴ n(A∩B) = 247

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 829 - 247 = 582

   n(A‘∪B‘)  = 582



7)  

 If A and B are two sets and U is the universal set such that n(U) = 956, n(A) = 368, n(B) = 337 and n(A∪B) = 440,

find n(A‘∪B‘).

Answer: 691


SOLUTION 1 :

 Given :

n(U) = 956

n(A) = 368

n(B) = 337

   n(A∪B) = 440,

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)

          = 368 + 337 - 440

         = 705 - 440 = 265

∴ n(A∩B) = 265

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 956 - 265 = 691

   n(A‘∪B‘)  = 691



8)  

 If A and B are two sets and U is the universal set such that n(U) = 886, n(A) = 368, n(B) = 334 and n(A∪B) = 499,

find n(A‘∪B‘).

Answer: 683


SOLUTION 1 :

 Given :

n(U) = 886

n(A) = 368

n(B) = 334

   n(A∪B) = 499,

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)

          = 368 + 334 - 499

         = 702 - 499 = 203

∴ n(A∩B) = 203

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 886 - 203 = 683

   n(A‘∪B‘)  = 683



9)  

 If A and B are two sets and U is the universal set such that n(U) = 852, n(A) = 351, n(B) = 447 and n(A∪B) = 416,

find n(A‘∪B‘).

Answer: 470


SOLUTION 1 :

 Given :

n(U) = 852

n(A) = 351

n(B) = 447

   n(A∪B) = 416,

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)

          = 351 + 447 - 416

         = 798 - 416 = 382

∴ n(A∩B) = 382

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 852 - 382 = 470

   n(A‘∪B‘)  = 470



10)  

 If A and B are two sets and U is the universal set such that n(U) = 929, n(A) = 307, n(B) = 452 and n(A∪B) = 451,

find n(A‘∪B‘).

Answer: 621


SOLUTION 1 :

 Given :

n(U) = 929

n(A) = 307

n(B) = 452

   n(A∪B) = 451,

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)

          = 307 + 452 - 451

         = 759 - 451 = 308

∴ n(A∩B) = 308

 n(A‘B‘) = n[(AB)‘]

                  = n(U) - n(AB)

      = 929 - 308 = 621

   n(A‘∪B‘)  = 621