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Let R be a reflexive relation on a finite set A containing n elements, and suppose R has m ordered pairs. Which statement must be true?

1. m is at least n
2. m is at most n
3. m equals n
4. none of these

Correct answer: m is at least n

Solution

A reflexive relation requires that every element in the set A is related to itself, which means there must be at least n ordered pairs corresponding to the n elements in A. Therefore, the total number of ordered pairs m must be at least n.

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