Question

Assume the variables \(x=5, y=6,\) and \(z=8 .\) Indicate by circling the \(T\) or \(F\) whether each of the following conditions is true or false: $$2 \quad !=y \quad \& \& \quad z \quad !=4$$

Short answer

Answer: True (T)

Step-by-step solution

Check the given values of \(x, y\) and \(z\)

We are given the values of the variables as \(x=5, y=6\) and \(z=8\).

Analyze the first inequality (\(2\) != \(y\))

We need to determine if the first inequality (2 is not equal to y) is true or false. We can check that directly by comparing the given value of \(y\) to 2. We have \(y = 6\). Since \(2\) != \(6\), the statement is True.

Analyze the second inequality (\(z\) != \(4\))

Now, we have to determine if the second inequality (z is not equal to 4) is true or false. We can check that directly by comparing the given value of \(z\) to 4. We have \(z = 8\). Since \(8\) != \(4\), the statement is True.

Combine the two inequalities using the 'AND' operator

The final step is to combine the two inequalities using the 'AND' operator. The 'AND' operator evaluates to True only if both statements are true. In this case, both inequalities are true based on our analysis in Step 2 and Step 3. Since both inequalities are True, the overall combined statement (\(2\) != \(y\) \(&\) \(z\) != \(4\)) is also True. Therefore, the answer is True (T).

Key concepts

Boolean logic in C++

In the realm of computer programming, particularly with C++, understanding Boolean logic is foundational to controlling program flow and making decisions. Boolean logic deals with the evaluation of expressions that result in either a true or false state. These expressions often involve relational operators like '==', '!=', '<', '>', '<=', and '>=' that compare values, aiding in this decision-making process.

Consider the exercise where we compare integer values using '!=' which denotes 'not equal to'. The expressions looked at were 2 != y and z != 4. Individually, each expression evaluates to either true (T) or false (F), and these are the fundamental outputs of Boolean logic in C++. Once these individual results are determined, they can be combined with logical operators to produce a final Boolean outcome.

Understanding C++ operators

C++ offers a rich set of operators that are symbols used for computations and value comparisons. There are arithmetic, relational, logical, bitwise, assignment and other types of operators that serve different purposes. In our exercise, we encountered the '!=' operator, which is a relational operator used for comparison, and it checks whether two values are unequal. If they are different, the result is true.

Logical operators, such as '&&' (AND), '||' (OR), and '!' (NOT), are used to combine multiple Boolean expressions. The AND operator, '&&', demands both conditions to be true for the resultant expression to be true. In contrast, the OR operator, '||', requires at least one condition to be true, while the NOT operator, '!', negates or inverts the truth value of a single Boolean expression.

C++ control structures

Control structures dictate the flow of execution in a C++ program. They include decision-making structures like if, else if, else statements, and switch cases, as well as looping structures like for, while, and do-while loops. These structures often rely on Boolean logic to decide which path of execution to follow.

For instance, an if statement will execute the code block that follows it only if the condition evaluates to true. The exercise's expressions using logical operators can often be found within these control structures to create more complex conditions. Mastering control structures is essential for writing effective and efficient programs, allowing developers to execute different blocks of code depending on whether certain conditions are met, or to repeat actions until specific conditions are no longer true.