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    • 2 years ago

    Can be proved that \(\emptyset \) is a subset of every set?

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    1. joemath314159
      • 2 years ago
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      Since the empty set contains no elements, the fact that:\[(\forall A), \emptyset\subseteq A\]is whats called vacuously true. In other words, its true by default, because there is nothing to check. It would be like going into a room of people where there are no cell phones, and saying "there are no cell phones on." That is vacuously true, because there arent any cell phones to check.

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