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
B
Symmetric
C
Transitive
D
None of these

Solution

## The correct option is B TransitiveSince $$x\nless x$$, 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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