Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {0, 4, 6, 8, 9}, and B = {0, 1, 2, 6, 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)'

To find the set (A' ∪ B)', we will use De Morgan's laws. According to De Morgan's laws, the complement of the union of two sets is equal to the intersection of their complements. So, (A' ∪ B)' = A ∩ B.

First, let's find the complements of sets A and B. The complement of a set is the set of all elements in the universal set that are not in the given set.

A' = U - A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} - {0, 4, 6, 8, 9} = {1, 2, 3, 5, 7} B' = U - B = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} - {0, 1, 2, 6, 9} = {3, 4, 5, 7, 8}

Now, let's find the union of A' and B':

A' ∪ B' = {1, 2, 3, 5, 7} ∪ {3, 4, 5, 7, 8} = {1, 2, 3, 4, 5, 7, 8}

Finally, let's find the complement of this union:

(A' ∪ B')' = U - (A' ∪ B') = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4, 5, 7, 8} = {0, 6, 9}

So, (A' ∪ B')' = {0, 6, 9}.