A={1,2,3,4}, THEN R={(1,2),(1,3),(3,3),(3,1)} IS A __________ans.REFLEXIVE RELATIONTRANSITIVE RELATIONNON SYMMETRIC RELATIONANTI SYMMETRIC RELATION Previous Marked for Review Next
Question
A={1,2,3,4}, THEN R={(1,2),(1,3),(3,3),(3,1)} IS A __________ans.REFLEXIVE RELATIONTRANSITIVE RELATIONNON SYMMETRIC RELATIONANTI SYMMETRIC RELATION Previous Marked for Review Next
Solution
The given set A={1,2,3,4} and relation R={(1,2),(1,3),(3,3),(3,1)} can be analyzed as follows:
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Reflexive Relation: A relation is reflexive if every element maps to itself. That is, all pairs (a,a) must be in R for all a in A. In this case, (1,1), (2,2), and (4,4) are not in R. So, R is not a reflexive relation.
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Transitive Relation: A relation is transitive if whenever an element a is related to an element b, and b is in turn related to an element c, then a is also related to c. In this case, we have (1,2) and (1,3) in R, but we do not have (2,3) in R. So, R is not a transitive relation.
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Symmetric Relation: A relation is symmetric if for every pair (a,b) in R, the pair (b,a) is also in R. In this case, we have (1,2) in R but we do not have (2,1) in R. So, R is not a symmetric relation.
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Anti-Symmetric Relation: A relation is anti-symmetric if whenever (a,b) and (b,a) are in R, then a = b. In this case, we have (3,1) and (1,3) in R, but 1 ≠ 3. So, R is not an anti-symmetric relation.
Therefore, the relation R is a non-symmetric relation.
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