The Department of Non-Conventional Energy Resources conducted a survey of 1110 families to know the number of families who use - Maths - Sets

Question

The Department of
Non-Conventional Energy Resources conducted a survey of 1110
families to know the number of families who use different types of
fuels as the means for cooking food In the survey, it was reported
that 600 families use LPG, 400 families use coal and 300 families
use wood 20 families use all the three types of fuels, 100 families
use both LPG and coal, and 80 families use both LPG and wood Also,
each family uses at least one of the three fuels How many families
use both coal and wood as a fuel for cooking
food?

Deepak · Accepted Answer

Let A, B,
C denote the sets of families who use LPG, coal, and
wood respectively as a fuel for cooking food Accordingly, we
have
n
(A
U
B
UC) = 1110,
n (A) =
600, n
(B) = 400,
n (C) =
300, n
(A
nB
nC) = 20,
n
(A
nB) = 100,
n (A
nC) = 80
We know that
n
(A
UB
UC) = n
(A) +
n (B)
+ n
(C) -n
(A
nB) -n
(A
nC) -n
(B
nC) +
n (A
nB
nC)
1110 = 600 + 400 + 300 -100 -80 -n
(B nC) +
20
1110 = 1140 -n (B
nC)
n
(B
nC) =
30
Thus, 30 families use both coal and
wood as a fuel for cooking food

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