For a set A with n elements, how many unordered pair-positions must be chosen to specify a symmetric relation?
Answer and explanation
Correct answer: n(n+1)/2
There are n diagonal positions, each representing one self-pair, and n(n−1)/2 unordered pairs of distinct elements. Each distinct pair must be chosen as a whole: either both orientations occur or neither occurs. Thus the total independent positions are n+n(n−1)/2=n(n+1)/2, yielding the corresponding power of two relations.
Frequently asked questions
What is the correct answer to this question?
n(n+1)/2
Why is this the correct answer?
There are n diagonal positions, each representing one self-pair, and n(n−1)/2 unordered pairs of distinct elements. Each distinct pair must be chosen as a whole: either both orientations occur or neither occurs. Thus the total independent positions are n+n(n−1)/2=n(n+1)/2, yielding the corresponding power of two relations.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
