Set Theory Formula

Consider that $A$,$B$ and $C$ are the sets, then

1.

$$A \cup A = A$$

2.

$$A \cap A = A$$

are called Idempotent Laws.

3.

$$A \cup B = B \cup A$$

4.

$$A \cap B = B \cap A$$

are called Commutative Laws.

5.

$$(A \cup B) \cup C = A \cup (B \cup C)$$

6.

$$(A \cup B) \cup C = A \cup (B \cup C)$$

are called Associative Laws.

7.

$$A \cup (B \cap C) = (A \cup B) \cap (A \cup C)$$

8.

$$A \cap (B \cup C) = (A \cap B) \cup (A \cap C)$$

are called Distributive Laws.

9.

$${(A \cup B)^C} = {A^C} \cap {B^C}$$

10.

$${(A \cap B)^C} = {A^C} \cup {B^C}$$

are called De-Morgan’s Laws.

11.

$$A - (B \cup C) = (A - B) \cap (A - C)$$

12.

$$A - (B \cap C) = (A - B) \cup (A - C)$$

13.

$$A - (B \cup C) = A \cap {(B \cup C)^C}$$

14.

$$A \cap (B - C) = (A \cap B) ? C$$

15.

$$A\Delta B = (A - B) \cup (B - A)$$

is called the Symmetric Difference.

16.

$$A \times (B \cup C) = (A \times B) \cup (A \times C)$$

17.

$$A \times (B \cap C) = (A \times B) \cap (A \times C)$$

18.

$$A \times (B - C) = (A \times B) - (A \times C)$$