Suppose A is a finite set with n elements. The number of elements and the rank…
2017
Suppose A is a finite set with n elements. The number of elements and the rank of the largest equivalence relation on A are
- A.
{n,1}
- B.
{n, n}
- C.
{n2, 1}
- D.
{1, n2}
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Correct answer: C
The largest equivalence relation on a set A with n elements is the universal relation, which contains all possible ordered pairs (a, b) where a, b ∈ A. Since there are n choices for the first element and n choices for the second, there are n² elements in this relation. This relation corresponds to a single equivalence class containing all elements of A, so the rank (number of equivalence classes) is 1.
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