Math  /  Discrete

Question9) Let XX be a set of three elements and P(X)\mathcal{P}(X) be the power set of XX. The digraph for one of the following relations on P(X)\mathcal{P}(X) has no loops. A) AR1BA \boldsymbol{R}_{\mathbf{1}} B iff A=BA=B B) AR2BA \boldsymbol{R}_{\mathbf{2}} B iff ABA \neq B C) AR3BA \boldsymbol{R}_{\mathbf{3}} B iff ABA \subseteq B D) AR4BA \boldsymbol{R}_{\mathbf{4}} B iff BAB \subseteq A E) NOTA

Studdy Solution
Based on the analysis, relation AR2B A \boldsymbol{R}_{\mathbf{2}} B iff AB A \neq B is the only one that results in a digraph with no loops.
The correct answer is:
B \boxed{B}

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