If A has 3 elements, how many symmetric relations on A are also reflexive?
Answer and explanation
Correct answer: 8
Option B is correct. Reflexivity forces all three diagonal pairs to be included. For a symmetric relation, each of the three off-diagonal unordered pairs, namely {1,2}, {1,3}, and {2,3}, may either be included in both directions or omitted in both directions. These three independent choices give 2^3=8 relations. Thus exactly eight relations are both symmetric and reflexive.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Option B is correct. Reflexivity forces all three diagonal pairs to be included. For a symmetric relation, each of the three off-diagonal unordered pairs, namely {1,2}, {1,3}, and {2,3}, may either be included in both directions or omitted in both directions. These three independent choices give 2^3=8 relations. Thus exactly eight relations are both symmetric and reflexive.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
