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Let us define a relation R in R as aRb if $a \geq b$.Then R is

\begin{array}{1 1}(a)\;an\;equivalance\;relation & (b)\;reflexive,transitive\;but\;not\;symmetric\\(c)\;symmetric,transitive\;but\;not\;reflexive & (d)\;neither\;symmetric\;nor\;transitive\end{array}

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  • A relation R in a set A is called $\mathbf{ reflexive},$ if $(a,a) \in R\;$ for every $\; a\in\;A$
  • A relation R in a set A is called $\mathbf{symmetric}$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$
  • A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$
  • 4. A relation R is an equivalnce relation if R is reflexive, symmetric and transitive
Given : Relation R is defined in R
$ a R b \;if \;a \geq b$
Consider $ a \in R$
Therefore a R a is true for all $a \in R$
R is reflexive
a R b
$=>a \geq b$
$=> b \leq a$
b R a is not true. if b < a
Therefore R is not symmetric
a R b and b R c
$ a \geq b\; and\; b \geq c$
$=> a \geq c$
Hence a R c
R is transitive
'B' option is correct
answered Mar 5, 2013 by meena.p
edited Mar 27, 2013 by meena.p

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