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Let $\mathrm{A}=\{\mathrm{a}, \mathrm{b}, \mathrm{c}\}$ and the relation $\mathrm{R}$ be defined on $\mathrm{A}$ as follows $R=\{(a, a),(b, c),(a, b)\}$
Then, write minimum number of ordered pairs to be added in $R$ to make $R$ reflexive and transitive.
Then, write minimum number of ordered pairs to be added in $R$ to make $R$ reflexive and transitive.
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Given relation, $\mathrm{R}=\{(\mathrm{a}, \mathrm{a}),(\mathrm{b}, \mathrm{c}),(\mathrm{a}, \mathrm{b})\}$.
To make $\mathrm{R}$ is reflexive we must add (b, b) and (c, c) to $\mathrm{R}$. Also, to make $\mathrm{R}$ is transitive we must add (a, c) to $\mathrm{R}$. So, minimum number of ordered pair is to be added are $(b, b),(c, c),(a, c)$.
To make $\mathrm{R}$ is reflexive we must add (b, b) and (c, c) to $\mathrm{R}$. Also, to make $\mathrm{R}$ is transitive we must add (a, c) to $\mathrm{R}$. So, minimum number of ordered pair is to be added are $(b, b),(c, c),(a, c)$.
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