Identify the rule of inference or the fallacy in each of the following logical arguments. v If it is cold, then we do not play golf. It is not cold. Therefore, we play golf. If 2P+ 1is a prime, then p=2". 2022 # 2". Therefore, 22022 + 1 is not a prime. If 2P 1is a prime, then p is a prime. 2110503 - 1 is a prime. Therefore, 110503 is a prime. We go to the beach only if it is sunny. It is sunny. Therefore, we go to the beach. If p is a prime, then 2P = 2 (mod p). 1. modus ponens 2. modus tollens 3. fallacy of affirming the conclusion 4. fallacy of denying the hypothesis

Identify the rule of inference or the fallacy in each of the following logical arguments. v If it is cold, then we do not play golf. It is not cold. Therefore, we play golf. If 2P+ 1is a prime, then p=2". 2022 # 2". Therefore, 22022 + 1 is not a prime. If 2P 1is a prime, then p is a prime. 2110503 - 1 is a prime. Therefore, 110503 is a prime. We go to the beach only if it is sunny. It is sunny. Therefore, we go to the beach. If p is a prime, then 2P = 2 (mod p). 1. modus ponens 2. modus tollens 3. fallacy of affirming the conclusion 4. fallacy of denying the hypothesis

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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5. What is the assumption (i.e., what you suppose) and what is the conclusion (i.e., what you need to show) in a proof by contrapositive of the following statement? "For any real number x, if 0 ≤ x ≤ 3, then 15-8x + x2 > 0." a. We suppose that x3. We must show that 15 - 8x + x2 ≤ 0. b. We suppose that x3. We must show that 15-8x + x2 ≤ 0. c. We suppose that 15 - 8x + x 2 ≤0. We must show that x 3. d. We suppose that 15-8x + x2 ≤0. We must show that x 3.
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Order the following sentences so that they form a direct proof of the statement: If x and y are rational numbers, then 3x + 2y is also a rational number. Choose from this list of sentences Since b, d are integers, bd is an integer. By the definition of rational numbers, x = a/b where a and b are integers and b# 0, and y = c/d where c and d are integers and d 0. Since 3x + 2y can be expressed as a ratio of two integers where the denominator is not zero, 3x + 2y is a rational number. Since a, b, c, d are integers, 3ad + 2bc is an integer. Let x and y be rational numbers. Since b 0 and d # 0, bd # 0. It follows that 3x + 2y = 3a/b + 2c/d = (3ad + 2bc)/(bd) Direct proof of the statement (in order):
5. Practice with RSA algorithma. Pick two prime numbers p, q, for example,• const int P=23;• const int Q=17;• int PQ=P*Q; b. Find a e that is relatively prime with (p-1)(q-1)Call RelativelyPrime () c. Calculate the inverse modulo (p-1)(q-1) of e to be your dUse inverse () c++
The options are even or odd.