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

Respuesta :

ivycoveredwalls
One version of DeMorgan's Laws:  [tex]\left( X \cap Y \right)' = X' \cup Y'[/tex].

In words: "the complement of the intersection of X and Y is equal to the union of their complements."

[tex]\left( A' \cap B \right)' = (A')' \cup B' = A \cup B'[/tex]

That last bit is due to the fact that the complement of the complement of A is A.   (A')' = A.

So take the union of A and B'.

[tex]A = \{ 0, 1, 4, 7, 9 \} \\ B' = \{1, 2, 3, 8, 9} \\ A \cup B' = \{ 0,1, 2,3,4,7,8,9 \}[/tex]

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