Theory question 101
SetsA, B and C are subsets of the universal set U such that:
U = {0, 1, 2, 3, ……, 12}
A = {x: 0 ≤ x ≤ 7}
B = {4, 6, 8, 10, 12}
C = {1 < y < 8}, where y is a prime number
(a) Draw a Venn diagram to illustrate the information given above.
(b) Find: (i) (B∪C)' (ii) A'∩B∩C
Show the model answer
Model answer
A = {0, 1, 2, 3, 4, 5, 6, 7}, B = {4, 6, 8, 10, 12}, C = {2, 3, 5, 7}.
(a) C lies inside A; A and B overlap in {4, 6}; B and C do not overlap. Place 0, 1 in A only; 2, 3, 5, 7 in C (inside A); 4, 6 in A∩B; 8, 10, 12 in B only; 9, 11 outside all three.
(b)(i) B∪C = {2, 3, 4, 5, 6, 7, 8, 10, 12}, so (B∪C)' = {0, 1, 9, 11}.
(ii) B∩C = ∅ (no even number in C is prime except 2, which is not in B), so A'∩B∩C = ∅ = { }.
Explanation
List each set in full before drawing the Venn diagram.