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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 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 $A.$
$\Rightarrow R$ is not antisymmetric on $A.$
Also$, R$ is not an identity relation on $A.$

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