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# LAWS OF SET OPERATIONS

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(1) Idempotent laws :

$$\text{A}\cap \text{A}=\text{A}$$

$$\text{A}\cup \text{A}=\text{A}$$

(2) Identity laws:

$$\displaystyle \text{A}\cap U\text{=A}$$

$$\text{A}\cup \phi =\text{A}$$

(3) Commutative laws:

$$\text{A}\cup \text{B}\,\text{=}\,\text{B}\cup \text{A}$$

$$\text{A}\cap \text{B}\,\text{=}\,\text{B}\cap \text{A}$$

(4) Associative laws:

$$\left( \text{A}\cup \text{B} \right)\cup \text{C}\,=\text{A}\cup \left( \text{B}\cup \text{C} \right)$$

$$\text{A}\cap \left( \text{B}\cap \text{C} \right)=\left( \text{A}\cap \text{B} \right)\cap \text{C}$$

(5) Distributive Laws:

$$\text{A}\cup \left( \text{B}\cap \text{C} \right)=\left( \text{A}\cup \text{B} \right)\cap \left( \text{A}\cup \text{C} \right)$$

$$\text{A}\cap \left( \text{B}\cup \text{C} \right)=\left( \text{A}\cap \text{B} \right)\cup \left( \text{A}\cap \text{C} \right)$$

(6) De-Morgan’s Laws:

$$\left( \text{A}\cup \text{B} \right)’=\text{A }\!\!’\!\!\text{ }\cap \text{B }\!\!’\!\!\text{ }$$

$$\left( \text{A}\cap \text{B} \right)’=\text{A }\!\!’\!\!\text{ }\cup \text{B }\!\!’\!\!\text{ }$$

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