Answered: 1. Let p, q, r, and s be propositional…

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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1. Let p, q, r, and s be propositional variables. Which of the following expressions are NOT correct formulas of propositional logic? Select all that apply.

p ¬ ∧ q ∧ r

p ∧ (q, r)

q ∨ s ∨ q

q¬r

2. Consider the propositions

p: You get an A on the Logic course
q: You pass the Algorithms course.

How would you write in propositional logic the natural language statement

You don't get an A on the Logic course and you pass the Algorithms course

¬p → q

¬p ∧ q

p ∧ ¬q

q → ¬p

3. The formula p → (p ∨ q) is _____.

true for two interpretations and false for the rest

valid

satisfiable but not valid

contradictory

4.The number of interpretations of a formula with 6 propositional variables is ___.

5.The formula (p ∨ q) ∧ r and the formula _____ are logically equivalent.

(p ∧ r) ∨ (q ∧ r)

(p ∨ r) ∧ (q ∧ r)

p ∨ (q ∧ r)

(p ∨ r) ∧ (p ∨ r)

6. Determine the equivalence law used in the expression; p and q denote propositional variables.

(p ∨ q)∧ (p ∨ q) ≡ (p ∨ q)

Group of answer choices

Absorption Law

Identity Law

Idempotent Law

Domination Law

7. Let u be a propositional variable. u ∧ T ≡ .

8. Let p and q be propositional variables. After simplification using equivalence laws, ¬((p ∧ T) ∨ (q ∧ F)) becomes ___.

¬p

9. In the choices of this question you are given the end of a branch (leaf) of a certain semantic tableau. Select the choice that represents a satisfiable formula.

¬p, r, ¬r, s

p, q, ¬p, r

¬p, ¬q, ¬r, r

¬p, ¬q, ¬r, ¬s

10. A section of a semantic tableau is given below. What is the value of the blank node?

q, ¬q

p, ¬q

¬p, ¬q

p, ¬p

Expert Solution

What is computer:

As per our guidelines we are supposed to answer only

? 3 sub- parts ( if there are multiple sub- parts asked )

Computer:

A computer is a digital electronic machine that can be programmed to automatically perform a series of arithmetic or logical operations (calculations).

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