$R = (1, 2), (2, 3), (34)$ be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is

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R = (1, 2), (2, 3), (34)

be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is

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solution: R = (1, 2), (2, 3), (3, 4) To make it an equivalence relation, we need to make it Reflexive, symmetric and transitive at the same time. Elements needed to make it Reflexive are (1, 1), (2, 2), (3, 3), (4, 4)

Elements related to make it symmetric are (2, 1), (3, 2), (4, 3) Elements needed to make it transitive are (1, 3), (2, 4) so total number of terms required are 9 Answer: option (c)

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Question Text	$R = (1, 2), (2, 3), (34)$ be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is
Answer Type	Text solution:1
Upvotes	150

R=(1,2),(2,3),(34) be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is

Text solutionVerified

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$R = (1, 2), (2, 3), (34)$ be a relation on the set of natural numbers. Then the last number of elements that must be included inn R to get a new relation S where S is an equivalence relation, is