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) = 884, n(A) = 361, n(B) = 478 and n(A∪B) = 401, find n(A‘∪B‘).
Answer:_______________ |
| 2) If A and B are two sets and U is the universal set such that n(U) = 769, n(A) = 380, n(B) = 436 and n(A∪B) = 493, find n(A‘∪B‘).
Answer:_______________ |
| 3) If A and B are two sets and U is the universal set such that n(U) = 824, n(A) = 344, n(B) = 421 and n(A∪B) = 414, find n(A‘∪B‘).
Answer:_______________ |
| 4) If A and B are two sets and U is the universal set such that n(U) = 740, n(A) = 367, n(B) = 404 and n(A∪B) = 457, find n(A‘∪B‘).
Answer:_______________ |
| 5) If A and B are two sets and U is the universal set such that n(U) = 772, n(A) = 369, n(B) = 334 and n(A∪B) = 460, find n(A‘∪B‘).
Answer:_______________ |
| 6) If A and B are two sets and U is the universal set such that n(U) = 748, n(A) = 356, n(B) = 369 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) = 979, n(A) = 311, n(B) = 491 and n(A∪B) = 406, find n(A‘∪B‘).
Answer:_______________ |
| 8) If A and B are two sets and U is the universal set such that n(U) = 781, n(A) = 345, n(B) = 358 and n(A∪B) = 438, find n(A‘∪B‘).
Answer:_______________ |
| 9) If A and B are two sets and U is the universal set such that n(U) = 962, n(A) = 315, n(B) = 360 and n(A∪B) = 464, find n(A‘∪B‘).
Answer:_______________ |
| 10) If A and B are two sets and U is the universal set such that n(U) = 822, n(A) = 310, n(B) = 410 and n(A∪B) = 404, find n(A‘∪B‘).
Answer:_______________ |
| 1) If A and B are two sets and U is the universal set such that n(U) = 884, n(A) = 361, n(B) = 478 and n(A∪B) = 401, find n(A‘∪B‘). Answer: 446 SOLUTION 1 : Given : n(U) = 884 n(A) = 361 n(B) = 478 n(A∪B) = 401, 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) = 361 + 478 - 401 = 839 - 401 = 438 ∴ n(A∩B) = 438 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 884 - 438 = 446 n(A‘∪B‘) = 446 |
| 2) If A and B are two sets and U is the universal set such that n(U) = 769, n(A) = 380, n(B) = 436 and n(A∪B) = 493, find n(A‘∪B‘). Answer: 446 SOLUTION 1 : Given : n(U) = 769 n(A) = 380 n(B) = 436 n(A∪B) = 493, 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) = 380 + 436 - 493 = 816 - 493 = 323 ∴ n(A∩B) = 323 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 769 - 323 = 446 n(A‘∪B‘) = 446 |
| 3) If A and B are two sets and U is the universal set such that n(U) = 824, n(A) = 344, n(B) = 421 and n(A∪B) = 414, find n(A‘∪B‘). Answer: 473 SOLUTION 1 : Given : n(U) = 824 n(A) = 344 n(B) = 421 n(A∪B) = 414, 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 + 421 - 414 = 765 - 414 = 351 ∴ n(A∩B) = 351 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 824 - 351 = 473 n(A‘∪B‘) = 473 |
| 4) If A and B are two sets and U is the universal set such that n(U) = 740, n(A) = 367, n(B) = 404 and n(A∪B) = 457, find n(A‘∪B‘). Answer: 426 SOLUTION 1 : Given : n(U) = 740 n(A) = 367 n(B) = 404 n(A∪B) = 457, 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 + 404 - 457 = 771 - 457 = 314 ∴ n(A∩B) = 314 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 740 - 314 = 426 n(A‘∪B‘) = 426 |
| 5) If A and B are two sets and U is the universal set such that n(U) = 772, n(A) = 369, n(B) = 334 and n(A∪B) = 460, find n(A‘∪B‘). Answer: 529 SOLUTION 1 : Given : n(U) = 772 n(A) = 369 n(B) = 334 n(A∪B) = 460, 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) = 369 + 334 - 460 = 703 - 460 = 243 ∴ n(A∩B) = 243 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 772 - 243 = 529 n(A‘∪B‘) = 529 |
| 6) If A and B are two sets and U is the universal set such that n(U) = 748, n(A) = 356, n(B) = 369 and n(A∪B) = 406, find n(A‘∪B‘). Answer: 429 SOLUTION 1 : Given : n(U) = 748 n(A) = 356 n(B) = 369 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) = 356 + 369 - 406 = 725 - 406 = 319 ∴ n(A∩B) = 319 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 748 - 319 = 429 n(A‘∪B‘) = 429 |
| 7) If A and B are two sets and U is the universal set such that n(U) = 979, n(A) = 311, n(B) = 491 and n(A∪B) = 406, find n(A‘∪B‘). Answer: 583 SOLUTION 1 : Given : n(U) = 979 n(A) = 311 n(B) = 491 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) = 311 + 491 - 406 = 802 - 406 = 396 ∴ n(A∩B) = 396 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 979 - 396 = 583 n(A‘∪B‘) = 583 |
| 8) If A and B are two sets and U is the universal set such that n(U) = 781, n(A) = 345, n(B) = 358 and n(A∪B) = 438, find n(A‘∪B‘). Answer: 516 SOLUTION 1 : Given : n(U) = 781 n(A) = 345 n(B) = 358 n(A∪B) = 438, 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) = 345 + 358 - 438 = 703 - 438 = 265 ∴ n(A∩B) = 265 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 781 - 265 = 516 n(A‘∪B‘) = 516 |
| 9) If A and B are two sets and U is the universal set such that n(U) = 962, n(A) = 315, n(B) = 360 and n(A∪B) = 464, find n(A‘∪B‘). Answer: 751 SOLUTION 1 : Given : n(U) = 962 n(A) = 315 n(B) = 360 n(A∪B) = 464, 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) = 315 + 360 - 464 = 675 - 464 = 211 ∴ n(A∩B) = 211 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 962 - 211 = 751 n(A‘∪B‘) = 751 |
| 10) If A and B are two sets and U is the universal set such that n(U) = 822, n(A) = 310, n(B) = 410 and n(A∪B) = 404, find n(A‘∪B‘). Answer: 506 SOLUTION 1 : Given : n(U) = 822 n(A) = 310 n(B) = 410 n(A∪B) = 404, 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 + 410 - 404 = 720 - 404 = 316 ∴ n(A∩B) = 316 n(A‘∪B‘) = n[(A∩B)‘] = n(U) - n(A∩B) = 822 - 316 = 506 n(A‘∪B‘) = 506 |