On A={1,2,3}, R={(1,1),(2,2),(3,3),(1,2),(2,1)}. Which statement is correct?
Answer and explanation
Correct answer: R is symmetric and reflexive
A relation R on A is reflexive when every diagonal pair (a,a) belongs to R, and it is symmetric when (a,b) in R implies (b,a) in R. Here (1,1), (2,2), and (3,3) are all present, so R is reflexive. The pair (1,2) occurs together with its reverse (2,1), and diagonal pairs reverse to themselves. Hence R is symmetric as well. Therefore option A is correct; options B and C contradict the listed pairs, while D does not state the required combined property.
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What is the correct answer to this question?
R is symmetric and reflexive
Why is this the correct answer?
A relation R on A is reflexive when every diagonal pair (a,a) belongs to R, and it is symmetric when (a,b) in R implies (b,a) in R. Here (1,1), (2,2), and (3,3) are all present, so R is reflexive. The pair (1,2) occurs together with its reverse (2,1), and diagonal pairs reverse to themselves. Hence R is symmetric as well. Therefore option A is correct; options B and C contradict the listed pairs, while D does not state the required combined property.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Relations and Functions. Topic: Symmetric relation.
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