Let X be a family of sets and R be a relation | vedclass

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(B) relation $R$ is defined on a family of sets $X$ such that $A R B$ if and only if $A \cap B = \emptyset$.$1$. Reflexivity: For $R$ to be reflexive,

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Symmetric

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(B) relation $R$ is defined on a family of sets $X$ such that $A R B$ if and only if $A \cap B = \emptyset$.$1$. Reflexivity: For $R$ to be reflexive,$A R A$ must hold for all $A \in X$. This implies $A \cap A = \emptyset$,which means $A = \emptyset$. Since this is not true for all sets in $X$,$R$ is not reflexive.$2$. Symmetry: If $A R B$,then $A \cap B = \emptyset$. Since intersection is commutative,$B \cap A = \emptyset$,which implies $B R A$. Thus,$R$ is symmetric.$3$. Transitivity: If $A R B$ and $B R C$,it does not necessarily imply $A R C$. For example,let $A = \{1\}$,$B = \{2\}$,and $C = \{1\}$. Here $A \cap B = \emptyset$ and $B \cap C = \emptyset$,but $A \cap C = \{1\} 
eq \emptyset$. Thus,$R$ is not transitive.Therefore,the relation $R$ is symmetric.

Let $X$ be a family of sets and $R$ be a relation defined on $X$ by "$A$ is disjoint from $B$". Then $R$ is:

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