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) 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.
Take Free Practice Test On 2026 JAMB UTME, Post UTME, WAEC SSCE, GCE, NECO SSCE
Correct Answer: Option n
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) \(U = n(H) + n(I) + n(Y) - n(H \cap Y) - n(H \cap I) - n(I \cap Y) + n(H \cap Y \cap I)\)
\(40 = 6 + x + 2 + x + 4 + x + 8 - x + 11 - x + 6 - x + x\)
\(40 = 37 + x \implies x = 40 - 37 = 3\)
(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) \(U = n(H) + n(I) + n(Y) - n(H \cap Y) - n(H \cap I) - n(I \cap Y) + n(H \cap Y \cap I)\)
\(40 = 6 + x + 2 + x + 4 + x + 8 - x + 11 - x + 6 - x + x\)
\(40 = 37 + x \implies x = 40 - 37 = 3\)