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Question

In the set $$A=\left\{ 1,2,3,4,5 \right\} $$, a relation $$R$$ is defined by $$R=\left\{ (x,y)|x,y\in A\quad and \quad x<y \right\} $$. Then $$R$$ is


A
Reflexive
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B
Symmetric
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C
Transitive
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D
None of these
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Solution

The correct option is B Transitive
Since $$x\nless  x$$, therefore $$R$$ is not reflexive. Also $$x< y$$
does not imply that $$y<x$$, So $$R$$ is not symmetric. Let $$xRy$$
and $$yRz$$. Then $$x<y$$ and $$y<z\Rightarrow x<z$$ i.e.,
$$xRz$$. hence $$R$$ is trasitive.

Mathematics

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