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Here is a proof by mathematical induction that any gathering of n people must all have the mame blood type Explain where the proof goes wrong Anchor If there is 1 person in the gathering everyone in the gathering obviously has the same blood type nductive hypothesis Assume that any gathering of k people must all have the same blood ype Inductive step Suppose k 1 people are gathered Send one of them out of the room The emaining k people must all have the same blood type by the inductive hypothesis Now bring the first person back and send someone else out of the room You get another gathering ofk people all of whom must have the same blood type Therefore all k 1 people must have the same blood type and we are done by mathematical induction lect one O a O b C The inductive hypothesis is falsc because there is no way to know the blood types of any group of k people The inductive step does not work for 3 people Sending them out of the room I aves 2 people but we cannot conclude that their blood types will match The inductive step does not work for 2 people Sending them out of the room leaves 1 person and 1 blood type but we cannot conclude that their blood types will match The anchor is false because there is no way to know the blood type of any 2 people

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