The relation "is subset of" on the power set | vedclass

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(B) The relation $R$ is defined as $A R B$ if $A \subseteq B$ for all $A, B \in P(A)$.$1$. Reflexive: Since $A \subseteq A$ for every $A \in P(A)$,the

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Anti-symmetric

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(B) The relation $R$ is defined as $A R B$ if $A \subseteq B$ for all $A, B \in P(A)$.$1$. Reflexive: Since $A \subseteq A$ for every $A \in P(A)$,the relation is reflexive.$2$. Anti-symmetric: If $A \subseteq B$ and $B \subseteq A$,then by the definition of set equality,$A = B$. Thus,the relation is anti-symmetric.$3$. Transitive: If $A \subseteq B$ and $B \subseteq C$,then $A \subseteq C$. Thus,the relation is transitive.Since the relation is reflexive,anti-symmetric,and transitive,it is a partial order relation,not an equivalence relation. Therefore,the correct option is $B$.

The relation "is subset of" on the power set $P(A)$ of a set $A$ is

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