Are De Morgan's laws for sets necessary in this proof?

[plum356]

Good evening!
Have a look at the following part of a proof:

Mentor note: Fixed the LaTeX
I don't understand the use of implications. Isn't $x\in C_M(A\cup B)\iff x\notin(A\cup B)$? To me, all of these predicates are equivalent.

 

[PeroK]

Good evening!
Have a look at the following part of a proof:
View attachment 293569
I don't understand the use of implications. Isn't $x\in C_M(A\cup B)\iff x\notin(A\cup B)$? To me, all of these predicates are equivalent.

Yes, these are all two-way implications.

For Latex you need double dollars or double hashes:$$x\in C_M(A\cup B)\iff x\notin(A\cup B)$$
Mentor note: Fixed the original post.

 

[PeroK]

 

[plum356]

Yes, these are all two-way implications.

For Latex you need double dollars or double hashes:$$x\in C_M(A\cup B)\iff x\notin(A\cup B)$$

$\text{Aha!}$
Thank you. :)