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

- at least one of the newspapers.
- neither Marathi nor English newspaper.
- Only one of the newspapers.

#### 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

**(i)** No. of individuals who read at least one of the newspapers

= n(M ∪ E) = 1750.

**(ii)** No. of individuals who read neither Marathi nor English newspaper

= n(M' ∩ E')

= n(M ∪ E)'

= n(X) - n(M ∪ E)

= 2000 - 1750

= 250.

**(iii)** 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.