4. (Laws of the Algebra of Propositions: De Morgan's Laws) (i) Construct the truth table of the proposition -(p^q). and then (ii) the truth table of the proposition P (as in the previous problem, both truth tables in (iii) must reflect the process of building of a compound proposition at hand from propositional variables). (iii) Compare the truth tables, and make a conclusion on the equivalence of the propositions, thereby proving that (p^q)=pVg

4. (Laws of the Algebra of Propositions: De Morgan's Laws) (i) Construct the truth table of the proposition -(p^q). and then (ii) the truth table of the proposition P (as in the previous problem, both truth tables in (iii) must reflect the process of building of a compound proposition at hand from propositional variables). (iii) Compare the truth tables, and make a conclusion on the equivalence of the propositions, thereby proving that (p^q)=pVg

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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Use propositional logic to prove that the argument is valid. (A→(B ∨ C))∧¬C→(A→B)
(b) Describe what Formal Logic consists of. Describe the set S = S(P) of formulas (wffs) of Propositional Logic (Calculus).
3) a) Given the Boolean equation X= ABC +ABC+ ABC + ABC +ĀBC with 8-cell map(K-map) answer the following questions À BC BC BC BC BC 1 A 1 = X i) What is the number of literals? ü) What is the number of min tems? i) Is the function a SOP or POS? iv) What is the number of variables in the function? v) Simplify X using the K-Map (vi) Draw the truth table for the function X = ABC + ABC + ABC. Use your truth table to draw the timing diagram for A, B, C and X +
9
6 due February 10). (a) Find the largest possible set of strings on the alphabet {c, d} that is pairwise distinguishable by the language L of strings not containing the substring cdd. Determine the index of L.
(Pythagorean Triples) A right triangle can have sides that are all integers. The set of threeinteger values for the sides of a right triangle is called a Pythagorean triple. These three sides mustsatisfy the relationship that the sum of the squares of two of the sides is equal to the square of thehypotenuse. Find all Pythagorean triples for side1, side2, and the hypotenuse all no larger than 500.Use a triple-nested for loop that simply tries all possibilities. This is an example of “brute-force”computing. It’s not aesthetically pleasing to many people. But there are many reasons why thesetechniques are important. First, with computing power increasing at such a phenomenal pace, solutions that would have taken years or even centuries of computer time to produce with the technology of just a few years ago can now be produced in hours, minutes or even seconds. Recentmicroprocessor chips can process a billion instructions per second! Second, as you’ll learn in moreadvanced computer science…
(c) Solve the following 8-puzzle problem by using heuristic search. You are required to indicate all working steps and marks will be given accordingly.
(Model Paper-II, Q5(a) | May-19(R16), Q4(b)) 40. Apply pumping lemma for the following language L = {a"|n is prime} and prove that it is not regular. OR tVuce joA T Prove that regular set L = {1Plp is a prime) is not regular. [Note: Assume a = 1 and n =p and solve the problem accordingly]. %3D Dec.-19(R16), Q5(a) State and prove pumping lemma for regular languages. Apply pumping lemma for the following language and prove that it is not regular L= {a"| n is prime}.