Unit Element

There is a unit element in Boolean Algebra, $U$

There is a zero element, $\varnothing$

$A \cap U = A$

$A \cup \varnothing = A$

(REJECT) From the logic, it seems these two elements cover the extremes of “everything” and ‘nothing”.

Another try, the first statement requires $U$ to be equal to A and possibly containing even more.

$\varnothing$ must be equal to A or smaller.

$A \cup A^{c} = U$

O.K., the above statement makes $U$ to be the “universe”, since the definition for $A^{c}$ , the complement of A, is “everything in the universe that isn’t in A”.

$A \cap A^{c} = \varnothing$

The above gives $\varnothing$ its “nothing” definition.

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