Complete the following formal proof by completing the inference rule references R₁ to R₁1-
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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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ac71798-dd20-457e-9df5-3bc404b8a2cf%2F3088ab2a-015e-45d7-bf77-70f10eb80255%2F82k7uyi_processed.png&w=3840&q=75)
Transcribed Image Text: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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