1.

out of 1000 student 658 failed in aggregate ,166 in aggregate and in group1 434 in aggregate and in group2 372 in group1 590 in group 2 and 126 in both the groups. how many failed in aggregate but not in group 2? a)106 b)224 c)206 d) 464​

Answer»

Step-by-step EXPLANATION:

Given out of 1000 student 658 failed in aggregate ,166 in aggregate and in group 1 434 in aggregate and in group 2 372 in group 1  590 in group 2 and 126 in both the groups. how many failed in aggregate but not in group 2?

  • Let A, B and C be THREE sets.
  • So NUMBER of elements of A n(A) = 658
  • So number of elements of B n(B) = 590
  • So number of elements of C n(C ) = 372
  • Now n(A Ո B) = 434
  • So n (B Ո C) = 126
  • So n (C Ո A) = 166
  • So n (A U B U C) = 1000
  • n (A U B U C)  = n(A) + n(B) + n(C) – n (A Ո B) – n (B Ո C) – n (C Ո A) +  n (A Ո B Ո C)
  •          1000 = 658 + 590 + 372 – 434 – 126 – 166 + n (A Ո B Ո C)
  •          1000 = 894 + n (A Ո B Ո C)
  •              1000 - 894 = n (A Ո B Ո C)
  •         Or n (A Ո B Ո C) = 106

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