In a class of 40 students, 25 speak Hausa, 16 speak Igbo, 21 speak Yoruba and each of the students speak at least one of the these three languages. If 8 speak Hausa and Igbo, 11 speak Hausa and Yoruba and 6 speak Igbo and Yoruba.
(a) Draw a Venn diagram to illustrate the information, using x to represent the number of students that speak all three languages.
(b) calculate the value of x.
Explanation
(a) The number that speak Hausa = n(H) = 25
The number that speak Igbo = n(I) = 16
The number that speak Yoruba = n(Y) = 21
Total no of students = U = 40
(n(H cap I) = 8 ; n(H cap Y) = 11 ; n(Y cap I) = 6)
(b) (U = n(H) + n(I) + n(Y) – n(H cap Y) – n(H cap I) – n(I cap Y) + n(H cap Y cap I))
(40 = 6 + x + 2 + x + 4 + x + 8 – x + 11 – x + 6 – x + x)
(40 = 37 + x implies x = 40 – 37 = 3)