I am basically trying to prove the Isomorphism between Sets and Propositions Pg 85 but a little bit more.
I like how the author gives the definitions of $A \cup B$, $A \cap B$ and $A'$ in the linked. He goes on to say "The operations of union, intersection and complementation of sets obey the identical laws within set theory to those obeyed by the logical connectives of OR, AND and NOT within the propositional calculus". And it is intuitive how he comes up with his "Conclusion: Sets and propositions are isomorphic to one another".
Is there a more succient way to show this isomorphism?
Furthermore I have been trying to show the isomorphism between $\wedge$ $\cup$ and $,$ in the following manner.
For the mapping the mapping $\varsigma: L_1 \vee L_2 \rightarrow L_1 \cup L_2$
we have:
$\forall x \in X$ and $\forall y \in Y$ we have $\varsigma(X \vee Y) = \{X,Y\} = \{X\} \cup \{Y\} = \varsigma(X) \cup \varsigma(Y)$.
Is this sufficient?