Question

Suppose that $\mathbf{x},\mathbf{y},\mathbf{z},$ and $\mathbf{w}$ are int variables, and $\mathbf{x}=3,\mathbf{y}=\mathbf{4},\mathbf{z}=\mathbf{7},$ and $\mathbf{w}=1$ What is the output of the following statements? a. cout << "x == y: " << (x == y) << endl; b. cout << "x != z: " << (x != z) << endl; c. cout << "y == z - 3: " << (y == z - 3) << endl; d. cout << "!(z > w): " << !(z > w) << endl; e. cout << "x + y < z: " << (x + y < z) << endl;

Short answer

a: false, b: true, c: true, d: false, e: false.

Step-by-step solution

Understand the Given Code

We need to evaluate boolean expressions in each print statement using the given integer values of variables. For each condition, evaluate whether it is true or false.

Evaluate Statement (a)

The statement is $cout<<"x==y:"<<(x==y)<<endl;$. Here, it checks if $x=3$ is equal to $y=4$. Since 3 is not equal to 4, the expression $(x==y)$ is false.

Evaluate Statement (b)

The statement is $cout<<"x!=z:"<<(x!=z)<<endl;$. It checks if $x=3$ is not equal to $z=7$. Since 3 is not equal to 7, the expression $(x!=z)$ is true.

Evaluate Statement (c)

The statement is $cout<<"y==z-3:"<<(y==z-3)<<endl;$. It checks if $y=4$ is equal to $z-3=7-3=4$. Since 4 is equal to 4, the expression $(y==z-3)$ is true.

Evaluate Statement (d)

The statement is $cout<<"!(z>w):"<<!(z>w)<<endl;$. It checks if $z=7$ is greater than $w=1$. Since this is true, $!(z>w)$ applies NOT to it, making the final result false.

Evaluate Statement (e)

The statement is $cout<<"x+y<z:"<<(x+y<z)<<endl;$. It checks if $x+y=3+4=7$ is less than $z=7$. Since 7 is not less than 7, the expression $(x+y<z)$ is false.

Key concepts

Boolean Expressions

In C++ programming, boolean expressions are used to evaluate conditions that result in a true or false outcome. These expressions play a critical role in decision-making processes within a program. For example, in the exercise, the expression $x==y$ checks if the values of variables $x$ and $y$ are equal. This is known as a relational boolean expression.
Boolean expressions can be composed of:

• Relational operators: ">", "<", ">=", "<=", "==", "!="
• Logical operators: "&&", "||", "!"

Using these operators, programmers can form complex conditions to control the flow of the program. Understanding how to construct and evaluate these expressions correctly is foundational in programming.

Variable Evaluation

Variable evaluation involves computing and substituting the current value of a variable within an expression. In our case, the variables $x$, $y$, $z$, and $w$ hold specific integer values: 3, 4, 7, and 1, respectively. When evaluating expressions such as $(y==z-3)$, it's essential to substitute these values to perform the calculation.
This process includes:

• Substituting values: Replace each variable with its corresponding value in the expression.
• Simple arithmetic: Perform any necessary arithmetic operations, like subtraction in $y==z-3$.

Effective variable evaluation ensures that logical conditions are tested accurately, producing reliable results in the program's execution.

Conditional Statements

Conditional statements in C++ allow a program to perform different actions based on the outcome of boolean expressions. They are critical for decision-making within the program.
The primary forms of conditional statements include:

• "if": Executes a block of code if a specified condition evaluates to true.
• "else": Provides alternative code execution if the "if" condition evaluates to false.
• "else if": Allows multiple conditions to be evaluated in sequence.

In our example, each condition is encapsulated within a `cout` statement to demonstrate its true or false result. However, in practice, these expressions would typically control the flow of logic, enabling the program to adapt dynamically to different scenarios.

Output Analysis

Output analysis involves understanding what the program will display to the user after evaluating and processing boolean expressions and variable values. The `cout` statements in C++ are used to print results to the console.
Focusing on:

• Expression results: Determine whether the output for each boolean operation will be true or false.
• Formatting: Ensure outputs are user-friendly, combining text with variable computation results (e.g., "x == y: 0" indicates that the condition is false).

This comprehension helps developers verify that their logic performs as expected and provides clear and helpful information to users. In the exercise, the output of statements like `!(z > w)` translates into a human-readable form, showing the direct outcome of the logic applied.