6. Let $A , B$ be finite sets, and define $d ( A , B ) = \operatorname { card } ( A \cup B ) - \operatorname { card } ( A \cap B )$ , where $\operatorname { card } ( A )$ denotes the number of elements in the finite set $A$. Proposition (1): For any finite sets $A , B$, ``$A \neq B$'' is a [Figure] necessary and sufficient condition for ``$d ( A , B ) > 0$''; Proposition (2): For any finite sets $A , B , C$, $d ( A , C ) \leq d ( A , B ) + d ( B , C )$. A. Both Proposition (1) and Proposition (2) are true B. Both Proposition (1) and Proposition (2) are false C. Proposition (1) is true, Proposition (2) is false D. Proposition (1) is false, Proposition (2) is true
6. Let $A , B$ be finite sets, and define $d ( A , B ) = \operatorname { card } ( A \cup B ) - \operatorname { card } ( A \cap B )$ , where $\operatorname { card } ( A )$ denotes the number of elements in the finite set $A$.
Proposition (1): For any finite sets $A , B$, ``$A \neq B$'' is a\\
\includegraphics[max width=\textwidth, alt={}, center]{dc06d11b-7713-423c-95b9-1351bb88518a-1_428_333_1338_1324}
necessary and sufficient condition for ``$d ( A , B ) > 0$'';
Proposition (2): For any finite sets $A , B , C$, $d ( A , C ) \leq d ( A , B ) + d ( B , C )$.\\
A. Both Proposition (1) and Proposition (2) are true\\
B. Both Proposition (1) and Proposition (2) are false\\
C. Proposition (1) is true, Proposition (2) is false\\
D. Proposition (1) is false, Proposition (2) is true