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Set theory and Venn diagrams sheet
Essay frame

Of 200 students, 90 study Accounting, 80 Economics and 70 Maths; 30 take Accounting and Economics, 25 Accounting and Maths, 20 Economics and Maths, and 10 all three. Draw a Venn diagram and find how many take (a) at least one, (b) none, (c) Accounting only.

How to lay out the answer. Follow the frame, then write it in your own words.

  1. 1 · Define the sets. U = 200 students; A = Accounting, E = Economics, M = Maths.
  2. 2 · Draw the Venn diagram. [Three overlapping circles inside a rectangle; centre 10, pairs 20, 15, 10, singles 45, 40, 35, outside 25]
  3. 3 · Fill from the centre.
    • All three: 10.
    • Pairs only: 30 − 10 = 20, 25 − 10 = 15, 20 − 10 = 10.
    • Singles: 90 − 20 − 15 − 10 = 45; 80 − 20 − 10 − 10 = 40; 70 − 15 − 10 − 10 = 35.
  4. 4 · At least one. 90 + 80 + 70 − 30 − 25 − 20 + 10 = 175.
  5. 5 · None. 200 − 175 = 25.
  6. 6 · Accounting only. 45.
  7. 7 · Check. 45 + 40 + 35 + 20 + 15 + 10 + 10 + 25 = 200. ✓