On A={1,2,3}, let R={(1,2),(2,1)}. Which is the most accurate description of R?
Answer and explanation
Correct answer: Symmetric and irreflexive
The correct answer is A. Whenever (1,2) belongs to R, its reversed pair (2,1) also belongs to R, so R is symmetric. However, none of (1,1), (2,2), or (3,3) is present, so no element is related to itself; thus R is irreflexive, not reflexive. Therefore B and C are wrong, while D is wrong because the relation is clearly symmetric.
Frequently asked questions
What is the correct answer to this question?
Symmetric and irreflexive
Why is this the correct answer?
The correct answer is A. Whenever (1,2) belongs to R, its reversed pair (2,1) also belongs to R, so R is symmetric. However, none of (1,1), (2,2), or (3,3) is present, so no element is related to itself; thus R is irreflexive, not reflexive. Therefore B and C are wrong, while D is wrong because the relation is clearly 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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