If A has 3 elements, how many antisymmetric relations are possible on A?
Answer and explanation
Correct answer: 2^9
For each of the three diagonal pairs, (a,a) may be chosen or not, giving 2^3 choices. For each of the three unordered distinct pairs, antisymmetry permits four choices: neither direction, only the first direction, only the reverse direction, or both directions are forbidden. Hence the count is 2^3×4^3=2^3×2^6=2^9, so C is correct.
Frequently asked questions
What is the correct answer to this question?
2^9
Why is this the correct answer?
For each of the three diagonal pairs, (a,a) may be chosen or not, giving 2^3 choices. For each of the three unordered distinct pairs, antisymmetry permits four choices: neither direction, only the first direction, only the reverse direction, or both directions are forbidden. Hence the count is 2^3×4^3=2^3×2^6=2^9, so C is correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
