\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$

$a=a$

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

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