Can anyone help me understand the answer to this set theory question?
Essentially, I read (A n B)' as everything that is not in A and B. Which would make sense why only the intersecting area of the circles is not included.
However, I read (A' u B') as everything not in A or not in B, which to me would mean elements not in circle A, not in circle B, and not in both. Similar to how logic gates work in electronics, where or would mean 'one or the other, or both'.
So can anyone explain how (A' u B') satisfies the following shaded area? Why are the singular sections of A and B included? I would have thought this equation only highlights the outside of the circles Ω.
Note: Im not disputing the answer, I know its correct, I just can't visualise why.
Best Answer
$B'$ is the purple area.
$A'$ is the green-blue area.
$A'\cup B'=\Omega\setminus (A\cap B)=(A\cap B)'$.