Step-by-step explanation:
Let A be the set of people who speak English.
B be the set of people who speak French.
A - B be the set of people who speak English and not French.
B - A be the set of people who speak French and not English.
A ∩ B be the set of people who speak both French and English.
Given
n(A) = 72 n(B) = 43 n(A ∪ B) = 100
Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
= 72 + 43 - 100
= 72 + 43 - 100
= 115 - 100
= 15
Therefore, Number of persons who speak both French and English
= 15
n(A) = n(A - B) + n(A ∩ B)
⇒ n(A - B) = n(A) - n(A ∩ B)
= 72 - 15
= 57
and n(B - A) = n(B) - n(A ∩ B)
= 43 - 15 = 28
Therefore, Number of people speaking English only = 57
Number of people speaking French only = 28
