There are 26 students in Mrs Pietzs fifth grade class at the

There are 26 students in Mrs. Pietz\'s fifth grade class at the International School of Tokyo. All of the students speak either English or Japanese, and some speak both languages. If 18 of the students can speak English and 14 can speak Japanese, how many speak both English and Japanese? how many speak English, but not Japanese?

Solution

a) n(AUB) = n(A) + n(B) - n(A int B)

26 = 14 + 18 - n(A int B)

n(A int B) = 32 - 26 = 6

Hence 6 students both speak English and Japanese

b) Students speaking english but not japanese

n(English but not japanese) = n(A) - n(A int B)

=> 18 - 6

=> 12