The set of all Equivalence Classes of a set A of Cardinality C

2007

The set of all Equivalence Classes of a set A of Cardinality C

Answer: C. forms a partition of A — The set of all equivalence classes of a set A forms a partition of A. By definition, an equivalence relation divides the set into disjoint subsets such that…

  1. A.

    is of cardinality 2c

  2. B.

    have the same cardinality as A

  3. C.

    forms a partition of A

  4. D.

    is of cardinality C2

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Correct answer: C

The set of all equivalence classes of a set A forms a partition of A. By definition, an equivalence relation divides the set into disjoint subsets such that every element belongs to exactly one class. Thus, the union of all equivalence classes is equal to A.

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