Prove That All Distributive Law Is True for All $n \geq 3$

Short Answer

Prove that all distributive law $A _ { 1 } \cap \left( A _ { 2 } \cup \cdots \cup A _ { n } \right) = \left( A _ { 1 } \cap A _ { 2 } \right) \cup \cdots \cup \left( A _ { 1 } \cap A _ { n } \right)$ is true for all $n \geq 3$