On a set A with four elements, how many relations are both reflexive and antisymmetric?
Answer and explanation
Correct answer: 2^6
There are four compulsory diagonal pairs in a reflexive relation. Among the four elements, the number of unordered distinct pairs is C(4,2)=6. For each such pair, antisymmetry permits three possibilities: include the first direction, include the second direction, or include neither; it does not permit both. Therefore the count is 3^6, so none of the listed powers of two is correct unless the intended condition is different. To make the MCQ have one valid answer, the correct count should be 3^6; among the given choices, no option is mathematically correct.
Frequently asked questions
What is the correct answer to this question?
2^6
Why is this the correct answer?
There are four compulsory diagonal pairs in a reflexive relation. Among the four elements, the number of unordered distinct pairs is C(4,2)=6. For each such pair, antisymmetry permits three possibilities: include the first direction, include the second direction, or include neither; it does not permit both. Therefore the count is 3^6, so none of the listed powers of two is correct unless the intended condition is different. To make the MCQ have one valid answer, the correct count should be 3^6; among the given choices, no option is mathematically correct.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Types of relations.
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