4. Complete the following formal proof by completing the inference rule references R₁ to R11-1. {n>0} kn-1 {n>0^k=n-1}2. {n > 0^k=n-1}x= n {n> 0 Ak=n-1^x=n}3. n> 0 Ak=n-1^x=n⇒ p#Where p = 1 ≤k ≤n^x=n! / k!4. {n> 0 ^ k = n −-1} x == n {p}5. {n > 0} kn - 1; x =n {p}6. {p [x *k/x]} x == x * k {p}7. {p [x *k/x] [k - 1/k]} k = k-1 {p [x *k/x]}8. p^k>1⇒p [x*k / x] [k - 1/k]9. {p ^k> 1} k = k-1{p [x*k/x]}10. {p ^k> 1} k = k − 1; x = x * k {p}11. (inv p} W {p ^k ≤ 1}# Where W = while k > 1 do kk - 1; x = x * k od12. {n >0} k = n − 1; x =n (inv p} W {p ^ k ≤ 1}13.p ^k ≤ 1⇒ x = n!14. {n >0} k = n − 1; x = n {inv p} W {x = n!}R₁R₂predicate logicR3R4R5R6predicate logicR7RaR₂R10predicate logicR11

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Complete the following formal proof by completing the inference rule references R₁ to R₁1-

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

4. Complete the following formal proof by completing the inference rule references R₁ to R11-
1. {n>0} kn-1 {n>0^k=n-1}
2. {n > 0^k=n-1}x= n {n> 0 Ak=n-1^x=n}
3. n> 0 Ak=n-1^x=n⇒ p
#Where p = 1 ≤k ≤n^x=n! / k!
4. {n> 0 ^ k = n −-1} x == n {p}
5. {n > 0} kn - 1; x =n {p}
6. {p [x *k/x]} x == x * k {p}
7. {p [x *k/x] [k - 1/k]} k = k-1 {p [x *k/x]}
8. p^k>1⇒p [x*k / x] [k - 1/k]
9. {p ^k> 1} k = k-1{p [x*k/x]}
10. {p ^k> 1} k = k − 1; x = x * k {p}
11. (inv p} W {p ^k ≤ 1}
# Where W = while k > 1 do kk - 1; x = x * k od
12. {n >0} k = n − 1; x =n (inv p} W {p ^ k ≤ 1}
13.p ^k ≤ 1⇒ x = n!
14. {n >0} k = n − 1; x = n {inv p} W {x = n!}
R₁
R₂
predicate logic
R3
R4
R5
R6
predicate logic
R7
Ra
R₂
R10
predicate logic
R11

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