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Question
From amongst 2000 literate individuals of a town, 70% read Marathi newspapers, 50% read English newspapers and 32.5% read both Marathi and English newspapers. Find the number of individuals who read Only one of the newspapers
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Solution
Let M = set of individuals who read Marathi newspapers
E = set of individuals who read English newspapers
X = set of all literate individuals
∴ n(X) = 2000, n(M)
= `70/100xx2000`
= 1400
n(E) = `50/100xx2000` = 1000
n(M ∩ E) = `32.5/100xx2000` = 650
n(M ∪ E) = n(M) + n(E) − n(M ∩ E)
= 1400 + 1000 − 650
= 1750
No. of individuals who read only one of the newspapers
= n(M ∩ E’) + n(M’ ∩ E)
= n(M ∪ E) – n(M ∩ E)
= 1750 – 650
= 1100
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