Question

Question about DeMorgan's Laws:

The first part is "The intersection of the complements is equal to the complement of the union..."

I would write A' intersect B' intersect C' = (A U B U C)' right?

Answer 1

So my question is this. What if I have say: (A intersect B' intersect C) .. is this equal to
(A' U B U C')' ? Or is does DeMorgans not apply to a case where they are mixed complements and not?

Answer 2

yes, it still works
in
\[ A \cap B' = (A' \cup (B')' )'\]
But we know B''= B (the complement of the complement is the original)
so we get
\[ A \cap B' = (A' \cup (B')' )' = (A' \cup B) '\]

Answer 3

Thanks!