Let R = {( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 3 )} be a relation defined on the set { 1 , 2 , 3 , 4 } . Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation,

Question

Let R = {( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 3 )} be a relation defined on the set { 1 , 2 , 3 , 4 } . Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

TestHub · Accepted Answer

A = { 1 , 2 , 3 , 4 } For relation to be reflexive R = {( 1 , 2 ) , ( 2 , 3 ) , ( 3 , 3 )} Minimum elements added will be ( 1 , 1 ) , ( 2 , 2 ) , ( 4 , 4 ) ( 2 , 1 ) ( 3 , 2 ) ( 3 , 2 ) ( 3 , 1 ) ( 1 , 3 ) ∴ Minimum number of elements = 7

Mathematics - Sets and Relations Question with Solution | TestHub

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