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Recall that a preference relation is rational if it is complete and transitive:
#Completeness: <math>\forall x,y \in X: \quad x \succsim y \;\or\; y \succsim x</math>
#Transitivity: <math>\forall x,y,z \in X: \quad \mbox{if}\; \; x \succsim y \;\and\; y \succsim x z \;\mbox{then}\; x \succsim z</math>
Also recall the definition of the strict preference relation:
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