Question on: JAMB Mathematics - 2023
In a group of 500 people, 350 people can speak English, and 400 people can speak French. Find how many people can speak both languages.
A
750
B
850
C
250
D
150
Ask EduPadi AI for a detailed answer
Correct Option: C
Let \(F\) be the set of people who can speak French, and \(E\) be the set of people who can speak English.
Given that:
\[ n(F) = 400 \]
\[ n(E) = 350 \]
\[ n(F \cup E) = 500 \]
We want to find \(n(F \cap E)\) (the number of people who can speak both languages).
The inclusion-exclusion principle states:
\[ n(F \cup E) = n(F) + n(E) - n(F \cap E) \]
Substitute the given values:
\[ 500 = 400 + 350 - n(F \cap E) \]
Solve for \(n(F \cap E)\):
\[ n(F \cap E) = 750 - 500 = 250 \]
Therefore, \(250\) people can speak both languages.
So, the correct answer is 250.
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