# 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.$A \times (B – C) = (A \times B) – (A \times C)$