7. In a survey of 100 people it was found that 28 read magazine A, 30 read magazine B, 42 read magazine C, 8 read magazines A B, 10 read magazine AC 5 read magazine B and C and 3 read all the three. Find:i) How many read none of the magazines?ii) How many read magazine C only?
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Answer:
Step-by-step explanation:
Symbols used in ans:-
Union = U
Intersection = ^
. ☺☺☺♢♢♢♢♢●♢♢♢♢♢☺☺☺
Let set of Magazine A readers be A, B be B, and C be C.
.
Therefore,
n(U) = 100 ............ [ UNIVERSAL SET including both readers and non-readers ]
n(A) = 28
n(B) = 30
n(C) = 42
n(A^B) = 8
n(A^C) = 10
n(B^C) = 5
n(A^B^C) = 3
.
By the formula:-
n(AUBUC) = n(A) + n(B) + n(C) - n(A^B) - n(A^C) - n(B^C) + n(A^B^C)
n(AUBUC) = 28 + 30 + 42 - 8 - 10 - 5 + 3
Therefore total no. of readers = 80
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i) Hence total no. of people who dont read any magazine = 100 - 80 = 20
ii) No. of people who read only C = n(C) - n(A^C) - n(B^C) = 42 - 10 - 5 = 27
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