Proving DeMorgan's Second Rule

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SUMMARY

The discussion centers on proving DeMorgan's Second Rule, specifically the equation (A ∩ B)c = Ac ∪ Bc. The user successfully proved the first DeMorgan's rule and attempted to apply a similar method to the second rule. They expressed uncertainty about the correctness of their approach, particularly regarding the implications of the subsets A ⊆ B and B ⊆ A when A = B.

PREREQUISITES
  • Understanding of set theory concepts such as intersections and unions.
  • Familiarity with DeMorgan's Laws in logic and set theory.
  • Knowledge of subset relations and their implications.
  • Basic proof techniques in mathematics, particularly in set proofs.
NEXT STEPS
  • Study the formal proof of DeMorgan's Laws in set theory.
  • Explore examples of set proofs involving intersections and unions.
  • Learn about the implications of subset relations in set theory.
  • Practice proving mathematical statements using direct proof techniques.
USEFUL FOR

Students of mathematics, particularly those studying set theory and logic, as well as educators looking to reinforce concepts related to DeMorgan's Laws.

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Homework Statement


Hello, i proved the first demorgan's rule and using that i can easily proof the second one, but i tried to prove it as how i proved the first one. I would like to know what i did is correct, i feel i what i did might not be correct.


Homework Equations



(A \cap B)c = Ac \cup Bc

proving through the fact that if;

A=B
then following two should be satisfiable:
A\subsetB and B\subsetA



The Attempt at a Solution


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Seems correct!
 

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