Question

out of hundred percent in a group 72 person speak English and 43 person speaks French each one out of hundred percent 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​

Answer 1

Answer:

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 

                   = 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 

Thanks hope it helps