Out of 100 persons in a group, 72 persons speak English and 43 persons speak French. Each one out of 100 persons speak at least one language. Then how many speak only English? How many speak only French? How many of them speak English and French both?
Given: n(A) = 72, n(B) = 43 and n (A ∪ B) = 100
Total number of persons who speak at least one language = n (A ∪ B) = 100
n(A) = number of students who speaks English
n(B) = number of students who speaks French
n (A ∩ B) = number of students who speak both
As we know, n (A ∪ B) = n(A) + n(B) - n (A ∩ B)
⇒ n (A ∩ B) = 72 + 43 - 100
⇒ n (A ∩ B) = 115 - 100
⇒ n (A ∩ B) = 15
number of students who speak both the language = 15
number of students who speaks English only = 72 – 15 = 57
number of students who speaks French only = 43 – 15 = 28
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