For a set A with 3 elements, how many relations are not reflexive?
Answer and explanation
Correct answer: 448
Option A is correct. A three-element set gives 3²=9 possible ordered pairs, so there are 2^9=512 total relations. A reflexive relation must contain the three diagonal pairs, while the remaining six pairs may be selected freely, giving 2^6=64 reflexive relations. Hence the number of non-reflexive relations is 512−64=448.
Frequently asked questions
What is the correct answer to this question?
448
Why is this the correct answer?
Option A is correct. A three-element set gives 3²=9 possible ordered pairs, so there are 2^9=512 total relations. A reflexive relation must contain the three diagonal pairs, while the remaining six pairs may be selected freely, giving 2^6=64 reflexive relations. Hence the number of non-reflexive relations is 512−64=448.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
