Q. 02(10): (a) Use rules of inference to show that the hypotheses "It is not raining or Marry has her umbrella," "Marry does not have her umbrella or she does not get wet," and "It is raining or Marry does not get wet" imply that "Marry does not get wet." (b) Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

Q. 02(10): (a) Use rules of inference to show that the hypotheses "It is not raining or Marry has her umbrella," "Marry does not have her umbrella or she does not get wet," and "It is raining or Marry does not get wet" imply that "Marry does not get wet." (b) Prove that there is a positive integer that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive?

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

See similar textbooks

Similar questions

Theory of Computation(Regular Language) (Q)We define a sequential transduction to be a transduction that can be described by a sequential transducer. Is the class of sequential transductions closed under intersection? If no, justify your answer by a counter-example. If yes, outline a proof.
John is training for a marathon and he can easily alternate between running a mile and walking a mile. If he runs for 2 miles in a row, he becomes fatigued, and must then walk for 2 miles in a row in order to no longer be fatigued. When he is fatigued, he can still alternate between running a mile and walking a mile, but if he runs 2 miles in a row while already fatigued, he will collapse on the side of the road. If he runs 3 miles in a row at any point, he will also collapse. Let the letter 'a' stand for John running 1 mile, and the letter 'b' stand for John walking 1 mile. Draw a DFA which accepts all possible runs in which John does not collapse on the side of the road.
Set ProofsProve or disprove the following claims.
2. (13-09-2022) Let n number of identical small boxes are there where each of the first i boxes contains a diamond and remaining ni are empty. Harry Potter got two magic sticks that can test whether a box is empty or not in a single touch, except that a magic stick vanishes if he tests it on an empty box. How Harry Potter knows the value of i using two magic sticks to determine all the boxes containing pearls using at most o(n) touches?
What do the two equations do in the image? Please explain in plain English and with Python or Java example code (or any programming language) if possible and/or provide usage examples with step-by-step explanations for the solution(s). Thanks in advance.
4. Prove by direct proof that "“The square of an even integer is even" uith .uithaut
3.
Long chain of friends: You are given a list of people, and statements of the form “x knows y”. You are asked to find, is there a chain of k distinct people, such as x1 knows x2, x2 knows x3, and xk-1 knows xk. Prove that this problem is NP-complete by using one of the known NP-complete problems (CLIQUE, 3-SAT, Hamiltonian Path, Hamiltonian Cycle, Independent Set, etc.)
1. Prove by induction that Vi > 1, (L*)' = L*. • Basis: ? • Inductive Hypothesis: ? • Complete the rest of the proof: ?
METHODS OF PROOF PROVE THE FOLLOWING: 1. By contradiction, prove that "for all real numbers x, if x is irrational, then -x is irrational. *Please provide a clear proof. THANK YOU.
PS: Please complete all of the subparts as they are all the same question and not in Handwritten paper.
1.1) Write a short computer program to calculate Cy for an Einstein solid and show these results as a graph of Cy/Nk vs. kT/e. Include three scenarios: The q > N limits and also the more general case which is applicable for 'any" q. Present your graph.