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.\[A \times (B – C) = (A \times B) – (A \times C)\]