Let L be the set of all lines in a plane and R be the relation in L�

1.	Let L be the set of all lines in a plane and R be the relation in L defined as = {(L1, L2 ) ∶ L1 is perpendicular to L2 }. Show that R is symmetric .
Answer» Given relation R is defined on L, where L is the set of all lines in a plane and defined by R = {(L₁, L₂ ) ∶ L₁ is perpendicular to L₂ }. Now, let L₁, L₂ ∈ L such that (L₁, L₂ ) ∈ R. ⇒ L₁ is perpendicular to L₂. ⇒ L₂ is perpendicular to L₁. ⇒ (L₂, L₁ ) ∈ R ∀ L₁, L₂ ∈ I Hence, relation R is symmetric.

Let L be the set of all lines in a plane and R be the relation in L defined as = {(L1, L2 ) ∶ L1 is perpendicular to L2 }. Show that R is symmetric .

Answer»

Given relation R is defined on L, where L is the set of all lines in a plane and defined by

R = {(L₁, L₂ ) ∶ L₁ is perpendicular to L₂ }.

Now, let L₁, L₂ ∈ L such that (L₁, L₂ ) ∈ R.

⇒ L₁ is perpendicular to L₂.

⇒ L₂ is perpendicular to L₁.

⇒ (L₂, L₁ ) ∈ R ∀ L₁, L₂ ∈ I

Hence, relation R is symmetric.

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Let L be the set of all lines in a plane and R be the relation in L defined as = {(L1, L2 ) ∶ L1 is perpendicular to L2 }. Show that R is symmetric .

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