Properties of Algebras of Sets

Theorem
If $$\mathfrak{A} \ $$ is an algebra of sets, then all of the following are true:


 * 1) The intersection of two sets in $$\mathfrak{A} \ $$ is in $$\mathfrak{A} \ $$.
 * 2) The difference of two sets in $$\mathfrak{A} \ $$ is in $$\mathfrak{A} \ $$.

Proof

 * 1) Follows from the Relative Complement part of De Morgan's laws.
 * 2) Follows from the Set Difference part of De Morgan's laws.