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

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The discussion centers on the use of implications in a proof involving set theory. Participants clarify that the statement "x ∈ C_M(A ∪ B) iff x ∉ (A ∪ B)" represents a two-way implication. The conversation also touches on the correct formatting for LaTeX in mathematical expressions. Overall, the participants confirm the equivalence of the predicates in question. Understanding these implications is deemed essential for the proof's validity.
plum356
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Good evening!
Have a look at the following part of a proof:
Screenshot_2021-12-04_21-05-46.png

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.
 
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plum356 said:
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.
 
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:welcome:
 
PeroK said:
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. :)
 

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