please send answer for part a i and ii 1. (a) Consider the following algorithm:Input: A number k 20Output: ??X +0Y +1while x k doX + x+1Y +Y * Xreturn Yi. Give the output of this algorithm in terms of the input.ii. Write a loop invariant for this algorithm.iii. State and use the While-loop invariance theorem to prove that this algorithmis correct with respect to the output you gave in Part i.iv. Rewrite the algorithm using a For-loop rather than a While-loop.(b) Derive the following judgement using natural deduction:A implies (B and C), B implies D, C implies E- A implies (D andE)State clearly all the rules that you use in your derivation.

Output is the factorial of given number k. Detailed explanation with all steps is given in next…

1. (a) Consider the following algorithm: Input: A number k >0 Output: ?? X +0 Y1 while x k do X +x+1 Y +Y * X return Y i. Give the output of this algorithm in terms of the input. ii. Write a loop invariant for this algorithm.

1. (a) Consider the following algorithm: Input: A number k >0 Output: ?? X +0 Y1 while x k do X +x+1 Y +Y * X return Y i. Give the output of this algorithm in terms of the input. ii. Write a loop invariant for this algorithm.

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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Concept explainers

Computational Systems

The computation systems can be defined as the systems that are capable of solving a problem that includes calculations either mathematical or logical, and are able to produce the result as an output. For example, a simple calculator that is given a set of numbers and operators as input and produces the result as an output can be defined as a computational system. The above example is a simple illustration only, the computational systems range from simple devices to complex devices such as the systems that control the SpaceX companies, Starlink satellites which are being quite recently seen in the skies at many places globally.

Question

please send answer for part a i and ii

1. (a) Consider the following algorithm:
Input: A number k 20
Output: ??
X +0
Y +1
while x k do
X + x+1
Y +Y * X
return Y
i. Give the output of this algorithm in terms of the input.
ii. Write a loop invariant for this algorithm.
iii. State and use the While-loop invariance theorem to prove that this algorithm
is correct with respect to the output you gave in Part i.
iv. Rewrite the algorithm using a For-loop rather than a While-loop.
(b) Derive the following judgement using natural deduction:
A implies (B and C), B implies D, C implies E- A implies (D andE)
State clearly all the rules that you use in your derivation.

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