Answer to Question #7549 in Combinatorics | Number Theory for Ingrid

Question

Given the sets
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {2, 4, 6, 7, 8}, and B = {4, 5, 7, 8, 9}, use De Morgan's Laws to find the indicated set. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.)
(A' ∩ B)'

Answer 1

(A' ∩ B)' = | Using De Morgan's Law | = A'' U B' = A U B' = A U (U/B) = {2, 4, 5, 6, 7} U ({0, 1, 2, 3, 4, 5, 6, 7, 8, 9}\{2, 4, 5, 7, 9}) = {2, 4, 5, 6, 7} U {0, 1, 3, 6, 8} = { 0, 1, 2, 3, 4, 5, 6, 7, 8 }.