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  4. The relation, R= (1,3),(3,5) is defined on the set with minimum number of elements of natural numbers. The minimum number of elements to be included in R so that R is equivalence, is:

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Q. The relation, $R=\{(1,3),(3,5)\}$ is defined on the set with minimum number of elements of natural numbers. The minimum number of elements to be included in $R$ so that $R$ is equivalence, is:

Sets, Relations, and Functions

Solution:

Recall the properties of equivalence relation.