Question

. In a group of 191 students, 10 are taking French, business and music, 36 are taking French and business, 20 are taking French and music, 18 are taking business and music, 65 are taking French, 76 are taking business, and 63 are taking music. Let F. B, M be the sets of students taking at least French, business, or music, respectively (i.e. that subject and possibly, but not necessarily, others). Find the number of students in the

Answer 1

Here, n(F) = number of students taking French = 65 n(B) = nuber of students taking Business = 76 n(M) = number of students taking music = 63 n (F intersection B) = 36 n (F intersection M) = 20 n(B intersection M) = 18 and n(F intersection B intersection M) = 10 so, n (F intersection B' intersection M') = n (F) - n(F intersection B) - n(F intersection M + (F intersection M intersection B = 65 - 36 - 20 + 10 = 19 n(B intersection F' intersection M') = n(B) - n(B intersection F) - n(B intersection m =M) + n(F intersection B intersection M) = 76 - 36 - 18 + 10 = 32 n(M intersection F' intersection B') = n(M) - n(M intersection B) - n(M intersection F + n (F intersection B intersection M) = 63 - 18 - 20 + 10 = 35 so, n (F increment B increment M) = n (F intersection B' intersection M')