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RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
Question
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is:
  1. Identify relation.
  2. Reflexive.
  3. Symmetric.
  4. Antisymmetric.
✓

Answer

  1. Reflexive.
Solution:
Reflexivity: Since $(\text{a, a})\in\text{R}\ \forall\ \text{a}\in\text{A},$ R is reflexive on A.
Symmetry: Since $(\text{a, b})\in\text{R}$ but $(\text{b, a})\notin\text{R,}$ is not symmetric on A.
⇒ R is not antisymmetric on A.
Also, R is not an identity relation on A.

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