If set A has 4 elements, how many reflexive relations are possible on A?
Answer and explanation
Correct answer: 2^12
For a set with n elements, a relation is a subset of the n² ordered pairs. Reflexivity requires all n diagonal pairs (a,a), while the remaining n² − n pairs may be chosen or omitted independently. For n = 4, there are 16 total pairs and 4 compulsory pairs, leaving 12 optional pairs. Therefore the number is 2^12, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
2^12
Why is this the correct answer?
For a set with n elements, a relation is a subset of the n² ordered pairs. Reflexivity requires all n diagonal pairs (a,a), while the remaining n² − n pairs may be chosen or omitted independently. For n = 4, there are 16 total pairs and 4 compulsory pairs, leaving 12 optional pairs. Therefore the number is 2^12, so option A is correct.
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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