Question: Please help with this! The following is an incorrect proof of For every natural number n 1, in every group of people, all the people
Please help with this!
The following is an incorrect proof of
For every natural number n 1, in every group of people, all the people have blue eyes
Proof by induction:
-Induction step: Let n be an arbitrary number and suppose that in every group of n people, all the people have blue eyes. Consider a group of n+1 people. Label the N+1 people as person1, person2, ......., person(n+1)
-Consider person2,....., person(n+1), this is a group of n people. By the induction assumption, all the people have blue eyes. In particular, person(n+1) has blue eyes and thus all n+1 people have blue eyes.
This induction proof is obviously incorrect. What's wrong with it?
A) The proof of the "true for n" step implying "true for n+1" step is not valid when n = 1
B) The statement should be that all eyes are brown
C) We didn't verify the base n = 1 case
D) We didn't verify the base n = 0 case
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