Question:

Here is a proof by mathematical induction that any gathering of n people must all have the same blood type. Explain where the pr

Here is a proof by mathematical induction that any gathering of n people must all have the
same 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.
Inductive hypothesis: Assume that any gathering of k people must all have the same blood
type.
Inductive step: Suppose k + 1 people are gathered. Send one of them out of the room. The
remaining 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
of k people, all of whom must have the same blood type. Therefore all k + I people must have
the same blood type, and we are done by mathematical induction.
Select one:
a.
The anchor is false, because there is no way to know the blood type of any 2 people.
O b.
The inductive hypothesis is false, because there is no way to know the blood types of
any group of k people.
C.
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.
O d.
The inductive step does not work for 3 people. Sending them out of the room leaves 2
people, but we cannot conclude that their blood types will match.

Here is a proof by mathematical induction that any gathering of n people must all have the same 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. Inductive hypothesis: Assume that any gathering of k people must all have the same blood type. Inductive step: Suppose k + 1 people are gathered. Send one of them out of the room. The remaining 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 of k people, all of whom must have the same blood type. Therefore all k + I people must have the same blood type, and we are done by mathematical induction. Select one: a. The anchor is false, because there is no way to know the blood type of any 2 people. O b. The inductive hypothesis is false, because there is no way to know the blood types of any group of k people. C. 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. O d. The inductive step does not work for 3 people. Sending them out of the room leaves 2 people, but we cannot conclude that their blood types will match.