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NCERT Class 12 · Ch 1 Exercise 1.1 · Q14

NCERT Class 12 Maths · Chapter 1 Relations And Functions · Exercise 1.1 Question 14

On lines in the xy-plane, L₁RL₂ iff they are parallel. Prove equivalence and find all lines related to y=2x+4. Use the textbook convention that coincident lines count as parallel.

💡 Concept Hints

  1. Identify the slope and make the parallelism convention explicit.
  2. Work through the definitions using the stated domain and codomain; justify a failed universal property with one valid counterexample.

✅ Step-by-Step Solution

Final Answer: {y=2x+c:c∈ℝ}.
  1. Under the inclusive parallelism convention every line is parallel to itself, proving reflexivity.
  2. Parallelism means equality of unoriented line direction, which is symmetric.
  3. Two lines parallel to the same line have the same direction, proving transitivity.
  4. All lines with the direction of y=2x+4 have slope 2, so the class is exactly y=2x+c, c∈ℝ, including the original line.

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