## Step:

- Given n+1 pens, remove one pen, the remaining n pens are black by the inductive hypothesis
- Call this set of n pens T1

- Replace the first pen and remove another, the remaining n pens are black by inductive hypothesis
- Call this set of n pens T2

- The union of T1 and T2 is the original set of n+1 pens. Both subsets are black, so entire set is black.

- Given n+1 pens, remove one pen, the remaining n pens are black by the inductive hypothesis

## What is wrong here?

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