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hotvette

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- Clarification on membership table of A subset B

This isn't hw, just clarification on what I see in the book. I understand how to produce the following table:

\begin{array}{|c|c|c|} \hline A & B & A \subseteq B \\ \hline 0 & 0 & 1\\ \hline 0 & 1 & 1\\ \hline 1 & 0 & 0 \\ \hline 1 & 1 & 1 \\ \hline \end{array} What I don't have is an intuitive feel for the result. Take the first row for example. If ##x \notin A## and ##x \notin B##, how can this imply ##A \subseteq B##. I'm picturing ##A## and ##B## as disjoint sets with ##x## somewhere outside of both. Clearly I have a conceptual misunderstanding. Can someone explain? |