Theory question 102
SetsThe sets A = {1, 3, 5, 7, 9, 11}, B = {2, 3, 5, 7, 11, 15} and C = {3, 6, 9, 12, 15} are subsets of ε = {1, 2, 3, ...., 15}
(a) Draw a Venn diagram to illustrate the given information. (b) Use your diagram to find: (i) C∩A' (ii) A'∩(B∪C).
Show the model answer
Model answer
(a) Regions: A∩B∩C = {3}; A∩B only = {5, 7, 11}; A∩C only = {9}; B∩C only = {15}; A only = {1}; B only = {2}; C only = {6, 12}; outside all = {4, 8, 10, 13, 14}.
(b)(i) C∩A' = {6, 12, 15}.
(ii) A'∩(B∪C) = {2, 6, 12, 15}.
Explanation
Place the element common to all three sets first, then work outwards.