Solution to Induction

WARNING: You should seriously try to answer this question before looking at the solution -- it's just a good study skill. Also, some answers on this page may be more brief than you would want to put down in an actual exam. If you want any type of partial credit, you should write more than just the solution.

1. Yes, there is a major flaw. In her induction step, Prudence removes two students from the set B, and selects a third student (r). This implies that n+1 3, yet in the base case, n = 1. Clearly, 1 + 1 is not greater than or equal to 3. Thus the base case is not sufficient to support the induction step. In other words, transitivity does not work for a set of two elements.
   
   
2. No. By logic and reasoning, the entire student body of a class graded on a curve cannot fail. Besides which, the TAs and the professor of this class are good teachers. If all students fail CS212, then that indicates that there is a failure on the part of the professor and the TAs, which contradicts the previous statement. Anyways, Prudence's theorem was invalid, so no conclusions can be drawn based on an invalid theorem.

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