Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm, iff l is perpendicular to m for all l in L. Then R is:

• A) Reflexive
• B) Symmetric
• C) Transitive
• D) None of these

To analyze the relation R defined on the set L of all straight lines in a plane, we need to evaluate its properties: reflexivity, symmetry, and transitivity.

Reflexivity

A relation is reflexive if every element is related to itself. In this case, a line cannot be perpendicular to itself. Therefore, R is not reflexive.

Symmetry

A relation is symmetric if for any lines l and m, if l is related to m (lRm), then m is also related to l (mRl). Since if line l is perpendicular to line m, then line m is also perpendicular to line l, R is symmetric.

Transitivity

A relation is transitive if whenever l is related to m and m is related to n, then l is also related to n. For lines, if l is perpendicular to m and m is perpendicular to n, it does not imply that l is perpendicular to n. Thus, R is not transitive.

Final Assessment

Based on the analysis:

• R is not reflexive.
• R is symmetric.
• R is not transitive.

Therefore, the correct answer is B) Symmetric.