1. sets prove question 1

(1) Prove that for any sets A and B ,

A = ( A n B ) u ( A n B' )

(2) Prove that A u B - A n B = ( A-(A n B ) u ( B - ( A n B ))

2. For #1: $\displaystyle \left( {B \cup B'} \right) = U\,\& \,A \cap U = A$

#2 Expand on this idea: $\displaystyle \left( {A \cup C} \right) - B = \left( {A \cup C} \right) \cap B'$

(1) Prove that for any sets A and B ,

A = ( A n B ) u ( A n B' )

(2) Prove that A u B - A n B = ( A-(A n B ) u ( B - ( A n B ))
hi
for example let A={1,2,3,4,5};B={2,4}
for the first question (AnB)= {2,4};B'={1,3,5}
Then (AUB)U(AnB')={1,2,3,4,5}=A
Therefore it is proved
for the second question (A-(AnB))={1,2,3,4,5} - {2,4}={1,3,5}
(B-(AnB))={2,4} - {2,4} = { }
Therefore (A-(AnB) U (B-(AnB)) ={1,3,5} U { } ={1,3,5}----------1
AuB = {1,2,3,4,5}
AnB = {2,4}
Therefore AuB - AnB ={1,2,3,4,5} - {2.4} = {1,3,5}---------------2
Hence 1=2
proved the second question
ok