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