JAMB Mathematics 2023 Paper

Concept:This is a set theory problem using the principle of inclusion-exclusion for two overlapping sets.Explanation:Let $F$ represent people who speak French and $E$ represent people who speak English.Given: $n(F) = 400$, $n(E) = 350$, and $n(F \cup E) = 500$.We need to find $n(F \cap E)$, the number who speak both languages.Use the formula: $n(F \cup E) = n(F) + n(E) - n(F \cap E)$.Substitute the known values: $500 = 400 + 350 - n(F \cap E)$.This gives: $500 = 750 - n(F \cap E)$.Therefore, $n(F \cap E) = 750 - 500 = 250$.Answer:250 people can speak both languages, so the correct option is C.