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 = { })