/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 46 What is the value of \(x\) after... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 46

What is the value of \(x\) after each of these statements is encountered in a computer program, if \(x=1\) before the statement is reached? a) if \(x+2=3\) then \(x :=x+1\) b) if \((x+1=3)\) OR \((2 x+2=3)\) then \(x :=x+1\) c) if \((2 x+3=5)\) AND \((3 x+4=7)\) then \(x :=x+1\) d) if \((x+1=2) X O R(x+2=3)\) then \(x :=x+1\) e) if \(x<2\) then \(x :=x+1\)

Short Answer

Expert verified
The value of x after all statements is 3.

Step by step solution

01

- Initial Value

The initial value of \(x\) is given as \(x = 1\).
02

- Evaluate statement a

Check the condition \(x + 2 = 3\): \[ 1 + 2 = 3 \] This is True. Therefore, execute the statement \(x := x + 1\): \[ x = 1 + 1 = 2 \] So after statement a, \(x = 2\).
03

- Evaluate statement b

Starting from \(x = 2\). Check the condition \((x + 1 = 3)\) OR \((2x + 2 = 3)\): \[ x + 1 = 2 + 1 = 3 \text{ (True)} \text{ or } 2x + 2 = 2(2) + 2 = 6 eq 3 \text{ (False)} \] Since the OR condition is satisfied by the first part being True, execute the statement \(x := x + 1\): \[ x = 2 + 1 = 3 \] So after statement b, \(x = 3\).
04

- Evaluate statement c

Starting from \(x = 3\). Check the condition \((2x + 3 = 5)\) AND \((3x + 4 = 7)\): \[ 2(3) + 3 = 6 + 3 = 9 eq 5 \text{ (False)} \text{ and } 3(3) + 4 = 9 + 4 = 13 eq 7 \text{ (False)} \] Since both parts of the AND condition are False, don't execute the statement. So after statement c, \(x = 3\).
05

- Evaluate statement d

Starting from \(x = 3\). Check \((x + 1 = 2) XOR (x + 2 = 3)\): \[ x + 1 = 3 + 1 = 4 eq 2 \text{ (False)} \text{ or } x + 2 = 3 + 2 = 5 eq 3 \text{ (False)} \] Since both parts are False, the XOR condition is False. Execute: \[ x = x \text{ (no change)} \] So after statement d, \(x = 3\).
06

- Evaluate statement e

Starting from \(x = 3\). Check the condition \(x < 2\): \[ x = 3 \text{ which is not less than 2 (False)} \] Since it is False, don't execute the statement. So after statement e, \(x = 3\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

initial value
The initial value is the starting point of any variable in a computer program. Understanding the initial value is crucial because it sets the stage for all subsequent operations on that variable. Here, the initial value of \(x\) is given as \(x = 1\). This means that before any conditional statements are executed, \(x\) is set to 1. Always pay attention to initial values, as they directly affect the outcome of all future computations. By knowing the initial value, you can predict the variable's behavior after each conditional statement.
evaluation of conditions
Evaluating conditions is the process of determining if a given statement is True or False. Every conditional statement contains a condition that must be evaluated before any action is taken. For example, in statement a, the condition \(x + 2 = 3\) is evaluated. Since \(1 + 2 = 3\), the condition is True, so the subsequent action (\(x := x + 1\)) is performed. Evaluating conditions correctly ensures that the right actions are taken in your program. To evaluate conditions effectively:
  • Break down the condition into simpler expressions
  • Substitute the current values of variables
  • Determine the boolean outcome (True or False)
logical operators
Logical operators are symbols or words used to connect conditions in a way that shapes how they are evaluated. The main logical operators include AND, OR, and XOR. Each operator has specific rules:
  • AND (&&): Both conditions must be True for the entire expression to be True.
  • OR (||): At least one of the conditions must be True for the entire expression to be True.
  • XOR (^): Only one of the conditions must be True (but not both) for the entire expression to be True.
Recognizing how these operators work helps you understand complex conditions in programming. For example, in statement b, the condition \((x + 1 = 3) OR (2x + 2 = 3)\) includes an OR operator. Since the first part is True, the OR condition is satisfied, leading to the execution of \(x := x + 1\).
statement execution
Statement execution occurs when the condition in a conditional statement evaluates to True. When a condition is met, the appropriate action specified by the statement is carried out. For instance, in statement e, the condition is \(x < 2\). Given \(x = 3\), the condition is False, so the statement \(x := x + 1\) is not executed. In general, here is how you handle statement execution:
  • Evaluate the condition first.
  • If True, execute the action linked to the condition.
  • If False, skip the action and move to the next statement.
Always remember to follow these steps carefully to ensure the correct execution flow.
step-by-step problem solving
Step-by-step problem solving is essential for understanding and solving programming challenges. Breaking down a problem into manageable steps makes it easier to solve. For our example:
  • Identify the initial value: Here, \(x = 1\)
  • Evaluate each condition in sequence: Go through each statement's condition logically.
  • Take action based on the condition's result: Execute or skip the statement as needed.
  • Track changes in the variable's value: Update the variable as actions are executed.
By following these steps methodically, you can solve complex problems more easily. For instance, we started with \(x = 1\) and evaluated conditions step-by-step for each statement, determining whether to execute the statement and then updating \(x\) appropriately. This systematic approach ensures clarity and accuracy in solving programming problems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Let \(C(x)\) be the statement " \(x\) has a cat," let \(D(x)\) be the statement " \(x\) has a dog," and let \(F(x)\) be the statement "x has a ferret." Express each of these statements in terms of \(C(x), D(x), F(x),\) quantifiers, and logical connectives. Let the domain consist of all students in your class. a) A student in your class has a cat, a dog, and a ferret. b) All students in your class have a cat, a dog, or a ferret. c) Some student in your class has a cat and a ferret, but not a dog. d) No student in your class has a cat, a dog, and a ferret. e) For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.

Express the negation of these propositions using quantifiers, and then express the negation in English. a) Some drivers do not obey the speed limit. b) All Swedish movies are serious. c) No one can keep a secret. d) There is someone in this class who does not have a good attitude.

Prove that there is no positive integer \(n\) such that \(n^{2}+\) \(n^{3}=100 .\)

Let \(S=x_{1} y_{1}+x_{2} y_{2}+\cdots+x_{n} y_{n},\) where \(x_{1}, x_{2}, \ldots, x_{n}\) and \(y_{1}, y_{2}, \ldots, y_{n}\) are orderings of two different sequences of positive real numbers, each containing \(n\) elements. a) Show that \(S\) takes its maximum value over all orderings of the two sequences when both sequences are sorted (so that the elements in each sequence are in nondecreasing order). b) Show that \(S\) takes its minimum value over all orderings of the two sequences when one sequence is sorted into nondecreasing order and the other is sorted into nonincreasing order.

Suppose that Prolog facts are used to define the predicates mother \((M, Y)\) and father \((F, X),\) which represent that \(M\) is the mother of \(Y\) and \(F\) is the father of \(X\) , respectively. Give a Prolog rule to define the predicate \(\operatorname{sibling}(X, Y)\) which represents that \(X\) and \(Y\) are siblings (that is, have the same mother and the same father).
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.