Set Theory Formula

Consider 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 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)