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Asked by Dev Last Modified
Answer 
number of people speak hindi, n(H)=250
number of people speak english, n(E)=200
n (HUE) = 400
n(HUE)= n(H) +n(E) -n(H∩E)
400 = 250+200 - n(H∩E)
=450-n(H∩E)
n(H∩E)=450-400= 50
Thus, 50 people can speak both Hindi and English.
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Let H be the set of people who speak Hindi, and
E be the set of people who speak English
∴ n(H ∪ E) = 400, n(H) = 250, n(E) = 200
n(H ∩ E) = ?
We know that:
n(H ∪ E) = n(H) + n(E) – n(H ∩ E)
∴ 400 = 250 + 200 – n(H ∩ E)
⇒ 400 = 450 – n(H ∩ E)
⇒ n(H ∩ E) = 450 – 400
∴ n(H ∩ E) = 50
Thus, 50 people can speak both Hindi and English.
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