For a reflexive relation on an n-element set A, how many ordered pairs are necessarily present before any optional pairs are added?
Answer and explanation
Correct answer: n
Reflexivity requires every element to be related to itself. For A={a1,a2,...,an}, the compulsory pairs are (a1,a1), (a2,a2), ..., (an,an), giving exactly n diagonal ordered pairs. All off-diagonal pairs may be chosen independently, but they are not compulsory. Therefore option A is correct; n^2 counts all possible positions in a relation, not the required diagonal pairs.
Frequently asked questions
What is the correct answer to this question?
n
Why is this the correct answer?
Reflexivity requires every element to be related to itself. For A={a1,a2,...,an}, the compulsory pairs are (a1,a1), (a2,a2), ..., (an,an), giving exactly n diagonal ordered pairs. All off-diagonal pairs may be chosen independently, but they are not compulsory. Therefore option A is correct; n^2 counts all possible positions in a relation, not the required diagonal pairs.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Reflexive relation.
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