I am learning about σ-algebra. I am looking at an example of a set F ⊂ Ω and the authors are proving that F is a σ-algebra.

Let |A| denote the number of elements of a set A ⊂ Ω. Then, F is defined as F = {A ⊂ Ω: either |A| is finite or |Ac| is finite. So, among other things, they trying to prove that in line with the standard definition of σ-algebra that if a subset B ⊂ F ⇒ Bc ⊂ F.

For THIS particular example, they are defining the **complement of |A| as |Ac|c = |A|**. I am unable to understand this particular equality. Can someone please explain how they came up with this equality?