Let L be the set of all lines in a plane and R be the relation on L defined as L₁ R L₂ if L₁ is perpendicular to L₂. Then R is: A. Reflexive B. Symmetric C. Transitive D. Equivalence Answer: B) Symmetric Explanation: A line cannot be perpendicular to itself (not reflexive). If L₁ ⊥ L₂, then L₂ ⊥ L₁ (symmetric). If L₁ ⊥ L₂ and L₂ ⊥ L₃, then L₁ is parallel to L₃, not perpendicular (not transitive).

imo class 12 relations and functions

Let L be the set of all lines in a plane and R be the relation on L defined as L₁ R L₂ if L₁ is perpendicular to L₂. Then R is:

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Let L be the set of all lines in a plane and R be the relation on L defined as L₁ R L₂ if L₁ is perpendicular to L₂. Then R is:

A. Reflexive
B. Symmetric
C. Transitive
D. Equivalence

Answer: B) Symmetric

Explanation: A line cannot be perpendicular to itself (not reflexive). If L₁ ⊥ L₂, then L₂ ⊥ L₁ (symmetric). If L₁ ⊥ L₂ and L₂ ⊥ L₃, then L₁ is parallel to L₃, not perpendicular (not transitive).

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