Sets — O/L Mathematics

How do I practise Sets?

1 question with a worked solution

1. In a class of 40 students, 25 study Science, 20 study Commerce, and 5 study neither subject. How many students study both subjects?
   1. A) 15
   2. B) 10
   3. C) 5
   4. D) 12
   Check my answer

   Correct answer: B) 10

   Total in union n(S ∪ C) = 40 - 5 = 35. By principle of inclusion-exclusion: n(S ∩ C) = n(S) + n(C) - n(S ∪ C) = 25 + 20 - 35 = 45 - 35 = 10.

   Show worked solution

   Step 1: Calculate number studying at least one subject: n(A ∪ B) = 40 - 5 = 35. Step 2: Apply formula: n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Step 3: Substitute: 35 = 25 + 20 - n(A ∩ B) → 35 = 45 - n(A ∩ B). Step 4: n(A ∩ B) = 45 - 35 = 10. Answer: 10.
   Modelled on: the O/L Mathematics examination pattern

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Where does Sets fit in the syllabus?

Grade 10 · Term 2 · Grade 11 · Term 3