- #1

- 58

- 0

## Main Question or Discussion Point

Hello.

We all know that DeMorgan's Law is as follows:

(A∪B)' = A'∩B'

and

(A∩B)' = A'∪B'

where ' refers to the complement of a set and A and B are both sets.

We also know that this can be extended to more than two terms.

Here is my logic:

(A∩B∪C)' = ((A∩B)∪C)' = (A∩B)'∩C' = A'∪B'∩C'

We all know that DeMorgan's Law is as follows:

(A∪B)' = A'∩B'

and

(A∩B)' = A'∪B'

where ' refers to the complement of a set and A and B are both sets.

We also know that this can be extended to more than two terms.

**My question is whether or not the following is true:**

(A∩B∪C)' = A'∪B'∩C'(A∩B∪C)' = A'∪B'∩C'

Here is my logic:

(A∩B∪C)' = ((A∩B)∪C)' = (A∩B)'∩C' = A'∪B'∩C'