Determine what is wrong with the given induction arguments. We will prove that, in any...

Determine what is wrong with the given induction arguments.

We will prove that, in any set of n persons, all people have the same age.

Clearly, all people in a set of 1 person have the same age, so statement is true if n = 1.

Now suppose that in any set of k people, all people have the same age. Let be a set of k + 1 people. Then, by the induction hypothesis, all people in each of the sets and have the same age. But then all have the same age, and likewise all have the same age. It follows that all have the same age. This completes the inductive step.

The principle of mathematical induction therefore shows that, for any positive integer n, all people in any set of n persons have the same age.