Single correct option
Consider the following statements about relations on the set of all straight lines in a plane:
1. "Is parallel to" (a line being parallel to itself) is an equivalence relation.
2. "Is perpendicular to" is a transitive relation.
Which of the statements is/are correct?
1. "Is parallel to" (a line being parallel to itself) is an equivalence relation.
2. "Is perpendicular to" is a transitive relation.
Which of the statements is/are correct?
- A. 1 only
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Show answer and solution
Answer: (A) 1 only
Parallelism is reflexive (by convention), symmetric and transitive, so statement 1 is true. Perpendicularity is symmetric but not transitive: if and then , not . So statement 2 is false.
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