This is an extra credit problem for the third exam, given Wednesday 3/31/10.
This is due by Monday, April 12. It will be worth up to 6 points, to be added
to the exam grade.
You must include the following signed statement with your answer:
On my honor as

Forms of mathematical induction
March 19, 2010
We have covered three forms of mathematical induction:
MI: (P (0) (P (n) = P (n + 1) = nP (n).
SMI: n(k < n P (k ) = P (n) = nP (n).
WO: S N S = = n S k < n k S ).
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Theorem 1. The principles MI, SMI and WO a

Induction sample
Notice that in the example below, the colored text would apply to any proof
by induction.
Theorem. For all n N, 0 + 1 + + n =
n(n+1)
.
2
Proof. We prove this by induction on n N. For each n N , let P(n) be
the statement 0 + 1 + . + n = n(

NAME:
Takehome problem
Sets and Logic Final Exam
Answer the problem stated below. Staple any extra sheets to the back of this one, and bring them to the
exam on Monday April 26 at 3:00 pm to be handed in with the inclass exam.
Sign the following statement