What is the greatest possible number of pairs in a relation on A={1,2,3,4} that is both symmetric and antisymmetric?
Answer and explanation
Correct answer: 4
Option B is correct. If a relation is symmetric, the presence of (a,b) forces (b,a). Antisymmetry forbids both of these when a and b are distinct, so no off-diagonal pair can be included. Only the four diagonal pairs (1,1),(2,2),(3,3),(4,4) may occur, and including all of them gives the greatest possible size: 4.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Option B is correct. If a relation is symmetric, the presence of (a,b) forces (b,a). Antisymmetry forbids both of these when a and b are distinct, so no off-diagonal pair can be included. Only the four diagonal pairs (1,1),(2,2),(3,3),(4,4) may occur, and including all of them gives the greatest possible size: 4.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Introduction to Relations.
