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Let P be some predicate. Check the box next to each scenario in which Vn € N, P(n) must be true. (a) P(0) holds and for every natural number k > 0, if P(k) does not hold, then there is some natural number i < k such that P(i) does not hold. ✓(b) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold. ✔(c) For every natural number k > 0, if P(i) holds for every natural number i < k, then P(k) holds. (d) For every natural number k, if P(i) holds for every natural number i

Let P be some predicate. Check the box next to each scenario in which Vn € N, P(n) must be true. (a) P(0) holds and for every natural number k > 0, if P(k) does not hold, then there is some natural number i < k such that P(i) does not hold. ✓(b) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold. ✔(c) For every natural number k > 0, if P(i) holds for every natural number i < k, then P(k) holds. (d) For every natural number k, if P(i) holds for every natural number i

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let P be some predicate. Check the box next to each scenario in which Vn N, P(n) must be true. P(0) holds and for every natural number k > 0, if P(k) does not hold, then there is some natural number i < k such that P(i) does not hold. ✓(a) ✓(b) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold. ✔(c) For every natural number k > 0, if P(i) holds for every natural number i <k, then P(k) holds. x (d) For every natural number k, if P(i) holds for every natural number i <k, then P(k) holds. ✓
Transcribed Image Text:Let P be some predicate. Check the box next to each scenario in which Vn N, P(n) must be true. P(0) holds and for every natural number k > 0, if P(k) does not hold, then there is some natural number i < k such that P(i) does not hold. ✓(a) ✓(b) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold. ✔(c) For every natural number k > 0, if P(i) holds for every natural number i <k, then P(k) holds. x (d) For every natural number k, if P(i) holds for every natural number i <k, then P(k) holds. ✓
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