A) Equivalence relation
B) Not an equivalence but partial order relation
C) Both equivalence and partial order relation
D) None of these
Correct Answer: B
Solution :
[b] (i)\[A\subseteq Aie,ARA,\forall A\in P(S)\] \[\therefore \] R is reflexive. (ii) \[A\subseteq BB\subseteq A\] \[\therefore ARBBRA\]. So R is not symmetric. (iii) ARB and BRA \[\Rightarrow A\subseteq B\] and \[B\subseteq A\Rightarrow A=B\] Thus, R is anti-symmetric. (iv) ARB and BRC \[\Rightarrow A\subseteq B\,\,and\,\,B\subseteq C\] \[\Rightarrow A\subseteq C\Rightarrow ARC\] \[\therefore \] R is transitive relation. Thus, R is partially ordered relation but not an equivalence relation.You need to login to perform this action.
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