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Question : 10
Total: 50
Let set X = { 1 , 2 , 3 } and a relation R is defined in X as:
R = { ( 1 , 3 ) , ( 2 , 2 ) , ( 3 , 2 ) } , then minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are
Solution: 👈: Video Solution
(i) R is reflexive if it contains { ( 1 , 1 ) , ( 2 , 2 ) and ( 3 , 3 ) } . Since, ( 2 , 2 ) ∈ R . So, we need to add ( 1 , 1 ) and ( 3 , 3 ) to make R reflexive.
(ii)R is symmetric if it contains { ( 2 , 2 ) , ( 1 , 3 ) , ( 3 , 1 ) , ( 3 , 2 ) , ( 2 , 3 ) } .
Since,{ ( 2 , 2 ) , ( 1 , 3 ) , ( 3 , 2 ) } ∈ R . So, we need to add ( 3 , 1 ) and ( 2 , 3 ) .
Thus, minimum ordered pairs which should be added in relationR to make it reflexive and symmetric are { ( 1 , 1 ) , ( 3 , 3 ) , ( 3 , 1 ) , ( 2 , 3 ) } .
(ii)
Since,
Thus, minimum ordered pairs which should be added in relation
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