MCQ
Let $R = \{(a, a), (b, b), (c, c), (a, b)\}$ be a relation on set $A = a, b, c.$ Then, $R$ is:
- AIdentify relation.
- ✓Reflexive.
- CSymmetric.
- DAntisymmetric.
✓
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 $A.$
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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