Suppose P(n) and S(n) are statements that depend on a natural number n. You are glven that some statements and implications are true. Which of these properties imply that P(n) is true for every natural number n > 1? 1. P(1), P(k) = S(2k) and S(k + 1) = P(k) for all k > 1 2 S(1), P(k) = S(2k) and S(k) = P(k) for all k > 1 3. P(1), P(k) = P(k + 3) and P(k) → P(2k) for all k 2 1 4. P(1), P(k + 1) = P(k), and P(k) → P(2k) tor all k > 1 5. P(1), P(2), P(k) = S(k +1), and S(k) = P(k + 1) for all k > 1 6. P(1), S(1), P(k) → S(k + 1), P(k) → S(k + 2) and S(k) → P(k+ 1) for all k 2 1
Suppose P(n) and S(n) are statements that depend on a natural number n. You are glven that some statements and implications are true. Which of these properties imply that P(n) is true for every natural number n > 1? 1. P(1), P(k) = S(2k) and S(k + 1) = P(k) for all k > 1 2 S(1), P(k) = S(2k) and S(k) = P(k) for all k > 1 3. P(1), P(k) = P(k + 3) and P(k) → P(2k) for all k 2 1 4. P(1), P(k + 1) = P(k), and P(k) → P(2k) tor all k > 1 5. P(1), P(2), P(k) = S(k +1), and S(k) = P(k + 1) for all k > 1 6. P(1), S(1), P(k) → S(k + 1), P(k) → S(k + 2) and S(k) → P(k+ 1) for all k 2 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose P(n) and S(n) are statements that depend on a natural number n. You are given that some statements and implications are true.
Which of these properties imply that P(n) is true for every natural number n 2 1?
v1. P(1), P(k) = S(2k) and S(k + 1) = P(k) for all k > 1
2 S(1), P(k) = S(2k) and S(k) = P(k) for all k > 1
3. P(1), P(k) → P(k +3) and P(k) → P(2k) for all k 2 1
4. P(1), P(k + 1) = P(k), and P(k) = P(2k) tor all k 2 1
5. P(1), P(2), P(k) = S(k+ 1), and S(k) = P(k + 1) for all k 2 1
6. P(1), S(1), P(k) = S(k + 1), P(k) → S(k +2) and S(k) = P(k + 1) for all k 2 1
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