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Also recall the definition of the strict preference relation:
:<math>x \succ y \quad \Leftrightarrow \quad x \succsim y \;\and\; y \not{\succsim} x</math>
 
Then suppose:
 
:<math>\forall j \ne i \in H \quad i \succ_j h \quad \forall h\ne i,j \in H\quad\mbox{(Everyone Loves Brad)}</math>
:<math>\{\emptyset\} \succ_i h \quad \forall h\ne i \in H\quad\mbox{(Brad would rather be alone)}</math>
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