A survey of 100 students in an institution shows that 80 students speak Hausa and 20 students speak Igbo, while only 9 students speak both language. How many students speak neither Hausa nor Igbo?
The correct answer is B. 9
Let's solve this problem step by step. We are given that in a survey of 100 students, 80 students speak Hausa, 20 students speak Igbo, and 9 students speak both languages. We want to find the number of students who speak neither Hausa nor Igbo.
We can use the principle of inclusion-exclusion to solve this problem. The principle of inclusion-exclusion states that for any two sets A and B, the number of elements in their union is given by:
|A ∪ B| = |A| + |B| - |A ∩ B|
In this case, we have two sets: the set of students who speak Hausa (set A) and the set of students who speak Igbo (set B). We are given that |A| = 80, |B| = 20, and |A ∩ B| = 9. Using the formula above, we can find the number of students who speak either Hausa or Igbo (or both):
|A ∪ B| = |A| + |B| - |A ∩ B|
= 80 + 20 - 9
= 91
Since there are a total of 100 students, the number of students who speak neither Hausa nor Igbo is 100 - 91 = 9.
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