LAWS OF SET OPERATIONS

(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{ }

Post Author: E-Maths