Question

Complaints about works canteen had been about Mess (M) Food (F) and Service (S). Total
complaints 173 were received as follows:-
n(M) = 110, n(F) = 55, n(S) = 67, n(Mn Fn S') = 20, n(MnSn F') = 11
and n(F n Sn M') = 16. Determine the complaints about all the three.
(a) 6 (b) 53
(c) 35
(d) None
​

Answer 1

Answer:

ans: 6

Step-by-step explanation:

173 = 110 + 55 + 67 - (20 + x) - ( 11 + x) - (16 + x) + x

173 = 232 - 20 - x - 16 - x - 11 - x + x

2x = 232 - 47 - 173

2x = 12

x = 6

Answer 2

The complaints about all the three is 6.

Step-by-step explanation:

Given:

  n(M) = 110, n(F) = 55, n(S) = 67, n(M n F n S') = 20, n(M n S n S') = 11, n(M u F u S) = 173 and n(F n S n M') = 16.

Let the complaints about all three be 'x' which is n(M n F n S)

Now we know that,

⇒ n(M u F u S) = n(M) + n(F) + n(S) - n(M n F) - n(M n S) - n(S n F) + n(M n F n S)

 ⇒ 173 = 67 + 110 + 55 - 11 - x - 20 - x - 16 - x + x

⇒ 173 = 232 - 47 - 2x

⇒ 2x = 12

⇒ x = 6

⇒ n(M n F n S) = 6