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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 neither Marathi and English newspaper
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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)
= `70/100 xx 2000`
= 1400
n(E) = `50/100 xx 2000` = 1000
n(M ∩ E) = `32.5/100 xx 2000` = 650
n(M ∪ E) = n(M) + n(E) – n(M ∩ E)
= 1400 + 1000 – 650
= 1750
No. of individuals who read neither Marathi nor English newspaper
= n(M' ∩ E')
= n(M ∪ E)'
= n(X) – n(M ∪ E)
= 2000 – 1750
= 250
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