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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 10 of 50
Marks: +1, -0
Let set X={1,2,3}X=\{1,2,3\} and a relation RR is defined in XX as:
R={(1,3),(2,2),(3,2)}R=\{(1,3),(2,2),(3,2)\}, then minimum ordered pairs which should be added in relation RR to make it reflexive and symmetric are
(i) {R}\{R\} is reflexive if it contains {(1,1),(2,2)\{(1,1),(2,2) and (3,3)}(3,3)\}. Since, (2,2)∈R(2,2) \in R. So, we need to add (1,1)(1,1) and (3,3)(3,3) to make RR reflexive.
(ii) {R}\{R\} is symmetric if it contains {(2,2),(1,3),(3,1),(3,2)\{(2,2),(1,3),(3,1),(3,2), (2,3)}(2,3)\}.
Since, {(2,2),(1,3),(3,2)}∈R\{(2,2),(1,3),(3,2)\} \in R. So, we need to add (3,1)(3,1) and (2,3)(2,3).
Thus, minimum ordered pairs which should be added in relation {R}\{R\} to make it reflexive and symmetric are {(1,1),(3,3),(3,1),(2,3)}\{(1,1),(3,3),(3,1),(2,3)\}.
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