Suppose A is a finite set with n elements. The number of elements in the…
1998
Suppose A is a finite set with n elements. The number of elements in the largest equivalence relation of A is?
- A.
n
- B.
n2
- C.
1
- D.
n+1
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Correct answer: B
The largest equivalence relation on a set A with n elements is the universal relation, where every element is related to every element.
Thus, all possible ordered pairs are included.
Number of ordered pairs on a set with n elements:
n×n=n2
Therefore, the number of elements in the largest equivalence relation is:
n2
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