A partition of a set is a collection of non-empty, disjoint subsets whose union equals the original set. In other words, a partition of a set is a way to break the set into smaller, non-overlapping pieces.

For the set B = {a, b, c, d}, there are 15 possible partitions, including:

  1. {{a}, {b}, {c}, {d}}
  2. {{a, b}, {c}, {d}}
  3. {{a, c}, {b}, {d}}
  4. {{a, d}, {b}, {c}}
  5. {{a, b, c}, {d}}
  6. {{a, b, d}, {c}}
  7. {{a, c, d}, {b}}
  8. {{b, c, d}, {a}}
  9. {{a, b}, {c, d}}
  10. {{a, c}, {b, d}}
  11. {{a, d}, {b, c}}
  12. {{a, b, c, d}}
  13. {{a}, {b, c, d}}
  14. {{b}, {a, c, d}}
  15. {{c}, {a, b, d}}

Each of these partitions satisfies the conditions of a partition, namely that each subset is non-empty, the subsets are disjoint, and their union equals the original set B.

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