Question, Prove by distributive law :
$\displaystyle a_{1} \cap ( a_2 \cup ... \cup a_n ) = ( a_1 \cap a_2 ) \cup ... \cup ( a_1 \cap a_n )$ is true for all n>= 3
any one got a clue on this problem? I am lost....
Question, Prove by distributive law :
$\displaystyle a_{1} \cap ( a_2 \cup ... \cup a_n ) = ( a_1 \cap a_2 ) \cup ... \cup ( a_1 \cap a_n )$ is true for all n>= 3
any one got a clue on this problem? I am lost....
Well, you know that
$\displaystyle a_1 \cap ( a_2 \cup a_3) = (a_1 \cap a_2) \cup (a_1 \cap a_3)$
So now consider the case for
$\displaystyle a_1 \cap ( a_2 \cup a_3 \cup a_4)$
Define a new set $\displaystyle a_5 = a_3 \cup a_4$.
What is $\displaystyle a_1 \cap ( a_2 \cup a_5)$?
-Dan