How many symmetric relations can be formed on A = {1, 2, 3}?
Answer and explanation
Correct answer: 2⁶
For a symmetric relation on an n-element set, each diagonal pair (a,a) can be selected independently, giving n choices of position. For each unordered pair of distinct elements, either both ordered pairs are included or both are excluded. There are n(n−1)/2 such unordered pairs, so the total number of independent choices is n + n(n−1)/2 = n(n+1)/2. For n = 3, this is 3 + 3 = 6, giving 2⁶ relations. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
2⁶
Why is this the correct answer?
For a symmetric relation on an n-element set, each diagonal pair (a,a) can be selected independently, giving n choices of position. For each unordered pair of distinct elements, either both ordered pairs are included or both are excluded. There are n(n−1)/2 such unordered pairs, so the total number of independent choices is n + n(n−1)/2 = n(n+1)/2. For n = 3, this is 3 + 3 = 6, giving 2⁶ relations. Hence option B is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
