A, B and C are subsets of the universal set U such that : \(U = {0, 1, 2, 3,…, 12}; A = {x : 0 \leq x \leq 7}; B = {4, 6, 8, 10, 12}; C = {1 < y < 8}\), where y is a prime number.
(a) Draw a venn diagram to illustrate the information given above;
(b) Find: (i) \((B \cup C)’\); (ii) \(A’ \cap B \cap C\).
Explanation
(a) 
(b) A = {0, 1, 2, 3, 4, 5, 6, 7}
B = {4, 6, 8, 10, 12}
C = {2, 3, 5, 7}
U = {0,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
(i) \(B \cup C = {2, 3, 4, 5, 6, 7, 8, 10, 12}\)
\((B \cup C)' = {0, 1, 9, 11}\)
(ii) \(A' = {8, 9, 10, 11, 12}\)
\(A' \cap B \cap C = { }\)