Carlos, Deborah, and Janet want to bake a cake. They are choosing among chocolate cake ( C ), vanilla cake ( V ), and red velvet cake (R ). The following table shows each person's preferences for cake flavors. The three friends decide to vote on the kind of cake they want and agree to bake the kind that wins by majority vote. Carlos Deborah Janet First choice Second choice C Third choice V C Suppose Carlos, Deborah, and Janet first vote on whether to bake a chocolate cake or a red velvet cake, and then they vote between vanilla cake and the winner from the previous vote. Between chocolate cake and red velvet cake, the majority will vote for , and between this winner and vanilla cake, the majority will vote for Now, suppose Carlos, Deborah, and Janet first vote on whether to bake a red velvet cake or a vanilla cake, and then they vote between chocolate cake and the winner from this vote. Between red velvet cake and vanilla cake, the majority will vote for , and between this winner and chocolate cake, the majority will vote for True or False: Carlos, Deborah, and Janet's democratic voting system produces transitive preferences. (Hint: Recall your answers to the previous questions.) O True O FalseCarlos, Deborah, and Janet want to bake a cake. They are choosing among chocolate cake ( C ), vanilla cake ( V ), and red velvet cake (R ). The following table shows each person's preferences for cake flavors. The three friends decide to vote on the kind of cake they want and agree to bake the kind that wins by majority vote. Carlos Deborah Janet First choice R Second choice C Third choice V R C Suppose Carlos, Deborah, and Janet first vote on whether to bake a chocolate cake or a red velvet cake, and then they vote between vanilla cake and the winner from the previous vote. Between chocolate cake and red velvet cake, the majority will vote for , and between this winner and vanilla cake, the majority will vote for Now, suppose Carlos, Deborah, and Janet first vote on whether to bake a red velvet cake or a vanilla cake, and then they vote between chocolate cake and the winner from this vote. Between red velvet cake and vanilla cake, the majority will vote for and between this winner and chocolate cake, the majority will vote for True or False chocolate cake and Janet's democratic voting system produces transitive preferences. (Hint: Recall your answers to the previous questions.) red velvet cake vanilla cake False
