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.
(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) \(U = n(H) + n(I) + n(Y) - n(H \cap Y) - n(H \cap I) - n(I \cap Y) + n(H \cap Y \cap I)\)
\(40 = 6 + x + 2 + x + 4 + x + 8 - x + 11 - x + 6 - x + x\)
\(40 = 37 + x \implies x = 40 - 37 = 3\)
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