Let A={1,2,3,4}. Which relation is symmetric and transitive but not reflexive on A?
Answer and explanation
Correct answer: R={(1,1),(2,2),(1,2),(2,1)}
Option A is correct. Within the subset {1,2}, the relation contains both directions (1,2) and (2,1), and it contains the required diagonal pairs (1,1) and (2,2). It is transitive because every possible composition among these pairs remains in the same displayed set. However, it is not reflexive on all of A because (3,3) and (4,4) are absent. Option B is not symmetric or transitive, option C is reflexive as well as symmetric and transitive, and option D is not symmetric.
Frequently asked questions
What is the correct answer to this question?
R={(1,1),(2,2),(1,2),(2,1)}
Why is this the correct answer?
Option A is correct. Within the subset {1,2}, the relation contains both directions (1,2) and (2,1), and it contains the required diagonal pairs (1,1) and (2,2). It is transitive because every possible composition among these pairs remains in the same displayed set. However, it is not reflexive on all of A because (3,3) and (4,4) are absent. Option B is not symmetric or transitive, option C is reflexive as well as symmetric and transitive, and option D is not symmetric.
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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