MATH135 Study Guide - Midterm Guide: Joule, Mathematical Induction, Hit106.9 Newcastle

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24 Oct 2018
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MATH135 Full Course Notes
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MATH135 Full Course Notes
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Math 135 fall 2015: midterm solutions: let a and b be statements. (a) complete the truth table below. A b a b a ( a) = b. You do not need to prove or disprove the statement. Consider the following statement to be proved by strong induction. an = 2n 1 for all n n. Verify the base case(s) and carefully state the inductive hypothesis. You do not need to complete the proof here but may want to think it through before answering parts (a) and (b). (a) base case(s): Solution: when n = 1, a1 is de ned as 1, and 2n 1 = 1. When n = 2, a2 is de ned as 3, and. So the statement is true in these cases. (b) inductive hypothesis: Solution: assume the statement is true for all integers i where 1 i k for some integer k 2. 1: an erroneous proof of a statement is given below.