5. The following is an incorrect proof of For every natural number n 1, in every

Question

5.

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

Explanation / Answer

here is 3 step in mathmatical induction

1) prove statement is true for initial value of n

2) assume sttement is true for any arbitrary natural number n

3) prove that statement is true for n+1

obiviously

In this induction very first step is missing that is we have to prove statement for n=1

thus option c is correct which is we didn't verify the base n=1 case

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