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Induction Say which of the following statement is correct. The implicit domain of all quantifiers is N =...

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Advance Math

Induction

Say which of the following statement is correct. The implicitdomain of all quantifiers is
N = {0, 1, 2, ...}. If you mark a statement as incorrect then statebriefly what the problem is.
1. If p(0) and ?n>0 (p(n) ? p(n+1)) then ?n p(n)
2. If p(1) and ?n>0 (p(n?1) ? p(n)) then ?n p(n)
3. If p(0) and ?n>0 (p(n?1) ? p(n)) then ?n>3 p(n)
4. If p(0) and ?n>0 (p(n?1) ? p(n+1)) then ?n p(2n)
5. If p(0) and ?n?0 (¬p(n) ? p(n+1)) then ?n p(n)

don't understand these questions.

Answer & Explanation Solved by verified expert
3.6 Ratings (452 Votes)
1 If p0 and n0 pn pn1 then n pnThis is the correct version of Induction Base case is true p0and then the induction step This implies pn is true for alln2 If p1 and n0 pn1 pn then n pnThis is wrong    See Answer
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