What is the correct notation for Boolean algebra is that defined by the power set (set of all subsets) of set {a,b} $$ (\{0,a,b,1 \}, C, \cap ,\cup, 0, 1) $$ or $$ (\{a,b\}, C, \cap ,\cup, 0, 1) $$ and what is the carrier set for this algebra?
Correct notation for field of sets
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elementary-set-theory
boolean-algebra
1 Answers
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By your own specification the carrier set is the power set $\mathcal P(\{a,b\})$ which is $\{\varnothing,\{a\},\{b\},\{a,b\}\}$.
So the algebra would be something like $$ (\mathcal P(\{a,b\}), (A\mapsto\{a,b\}\setminus A), \cap, \cup, \varnothing, \{a,b\} ) $$