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  • Let a set <img alt="\mathrm{A}=\mathrm{A}_{1} \cup \mathrm{A}_{2} \cup \ldots \cup \mathrm{A}_{k^{\prime}}$ where $\mathrm{A}_{i} \cap \mathrm{A}_{j}=\phi$ for $i \neq j, 1 \leq i, j \leq k" src="h

Let a set \mathrm{A}=\mathrm{A}_{1} \cup \mathrm{A}_{2} \cup \ldots \cup \mathrm{A}_{k^{\prime}}$ where $\mathrm{A}_{i} \cap \mathrm{A}_{j}=\phi$ for $i \neq j, 1 \leq i, j \leq k. Define the relation \mathrm{R} from A to A by \mathrm{R}=\left\{(x, y): y \in \mathrm{A}_{i}\right.  if and only if \left.x \in \mathrm{A}_{i}, 1 \leq i \leq k\right\}. Then, \mathrm{R} is :

Option: 1

reflexive, symmetric but not transitive


Option: 2

reflexive, transitive but not symmetric


Option: 3

reflexive but not symmetric and transitive


Option: 4

an equivalence relation


Answers (1)

As \mathrm{R} contains all ordered pairs of  \mathrm{A_{1}, A_{2}, A_{3}, \ldots A_{k} .}

So it must be an equivalence relation .

Hence the correct answer is option 4.

Posted by

Sumit Saini

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