A [ & ] B = 0 <==> A [ || ] B = A [ |o| ] B
[==>]
( x € A || x € B )
( x € A || x € B ) & ¬( x € A & x € B )
( x € A |o| x € B )
[<==]
( x € A & x € B )
( x € A || x € B )
( x € A |o| x € B )
( x € A || x € B ) & ¬( x € A & x € B )
A [ & ] B = 0 <==> A [ \ ] B = A
[==>]
x € A
x € A & ¬( x € A & x € B )
x € A & ( ¬( x € A ) || ¬( x € B ) )
( x € A & ¬( x € A ) ) || ( x € A & ¬( x € B ) )
0 || ( x € A & ¬( x € B ) )
( x € A & ¬( x € B ) )
[<==]
x € A & x € B
( x € A & ¬( x € B ) ) & x € B
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