Let R be the relation over the set of straight lines of a plane- such that l 1 R l 2- l 1- l 2- Then- R isA- symmetricB- reflexiveC- transitiveD- an equivalence relation

The correct option is A symmetricl_1 R l_1 ⇒ l_1 is not perpendicular to l_1 (∴ R is not reflexive) l_1 R l_2 ⇒ l_1 ± l_2 ⇒ l_2 R l_1 ⇒ l_2 R l_1 , Hence, R i ...

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Standard IX

Mathematics

Symmetric Relations

Let R be the ...

Question

Let R be the relation over the set of straight lines of a plane, such that $l_{1} R l_{2} \Leftrightarrow l_{1} \pm l_{2}$ . Then, R is

symmetric

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reflexive

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transitive

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an equivalence relation

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Solution

The correct option is A symmetric
$l_{1} R l_{1} \Rightarrow l_{1}$ is not perpendicular to $l_{1}$
( $∴$ R is not reflexive)
$l_{1} R l_{2} \Rightarrow l_{1} \pm l_{2}$
$\Rightarrow l_{2} R l_{1} \Rightarrow l_{2} R l_{1}$ , Hence, R is symmetric.
$l_{1} R l_{2}$ and $l_{2} R l_{3} / \Rightarrow l_{1} R l_{3}$ .( $∴$ R is not transitive)

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Let R be the relation over the set of straight lines of a plane, such that l1 R l2⇔l1±l2 . Then, R is

The correct option is A symmetricl1 R l1⇒l1 is not perpendicular to l1 (∴ R is not reflexive) l1 R l2⇒l1±l2 ⇒l2Rl1⇒l2Rl1 , Hence, R is symmetric. l1 R l2 and l2 R l3 /⇒l1 R l3 .(∴ R is not transitive)

Let R be the relation over the set of straight lines of a plane, such that $l_{1} R l_{2} \Leftrightarrow l_{1} \pm l_{2}$ . Then, R is