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  3. are the following statements true or false? 1. let

Are the following statements true or false? 1. Let P(n) be the statement "If any string...

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Advance Math

Are the following statements true or false?

1. Let P(n) be the statement "If any string of length n over {a,b} has more a's than b's, then it has two a's in a row". We canprove this statement is true for all n with n ? 2 by proving P(2),P(3), and "for all n: P(n) ? P(n+2)".

2. Let P(x) be a predicate with one free variable x of typenatural. If I prove P(0), "for all x: P(x) ?P(x+2)", and "for all x: P(x) ? P(x+3)", I may conclude "for all x:P(x)".

Answer & Explanation Solved by verified expert
3.7 Ratings (393 Votes)
1For n3 we take the stringaba of length3 It is a string overab that has more asthan bs but without two as ina row Thus P3 is not    See Answer
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