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1.
$A \sub I$
Sets
2.
$A \sub A$
Sets
3.
Empty set
$\emptyset \sub A$
Sets
4.
Union of sets
$A \cup B= \{x : x \in A \; \text{or} \; x \in B \}$
Sets
5.
Intersection of sets
$A \cap B= \{x : x \in A \; \text{and} \; x \in B \}$
Sets
6.
Difference of sets
$A \setminus B = \{ x : x\in A \, \text{and} \, x\notin B\}$
Sets
7.
Set commutativity
$A \cup B = B \cup A$
Sets
8.
Set commutativity
$A \cap B = B \cap A$
Sets
9.
Set associativity
$A \cup \left(B \cup C \right) = \left( A \cup B \right) \cup C$
Sets
10.
Set associativity
$A \cap \left(B \cap C \right) = \left( A \cap B \right) \cap C$
Sets
11.
Set distributivity
$A \cup \left(B \cap C\right) = \left(A \cup B \right) \cap \left(A \cup C \right)$
Sets
12.
Set distributivity
$A \cap \left(B \cup C\right) = \left(A \cap B \right) \cup \left(A \cap C \right)$
Sets
13.
Idempotency
$A \cup A = A$
Sets
14.
Idempotency
$A \cap A = A$
Sets
15.
Domination
$A \cap \empty = A$
Sets
16.
Domination
$A \cup I = I$
Sets
17.
identity
$A \cup \empty = A$
Sets
18.
Identity
$A \cap I = A$
Sets
19.
Complement
$A^\prime=\{x \in I : x \notin A\}$
Sets
20.
Complement of union
$A \cup A^\prime = I$
Sets

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