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Relations — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRelations1 Mark
MCQ
Let R = {(a, a), (b, b), (c, c), (a, b)} be a relation on set A = a, b, c. Then, R is:
  • A
    Identify relation.
  • ✓
    Reflexive.
  • C
    Symmetric.
  • D
    Antisymmetric.
✓

Answer

Correct option: B.
Reflexive.
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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