Question

Assume the variables \(x=5, y=6,\) and \(z=8 .\) Indicate if each of the following conditions is true or false: \(\begin{array}{ll}\text { A) } x>=0 & || x<=y\end{array}\) B) \(z-y>y\) C) \(1(z-y>x)\)

Short answer

Question: Given \(x = 5\), \(y = 6\), and \(z = 8\), determine if the following conditions are true or false: A) \(x \ge 0\) || \(x \le y\) B) \(z - y > y\) C) \((z - y > x)\) Answer: A) True B) False C) False

Step-by-step solution

Substitute given values:

We are given \(x = 5\), \(y = 6\), and \(z = 8\). We will substitute these values into each given condition.

Check Condition A:

Condition A: \(x \ge 0\) || \(x \le y\) Substitute the given values: \(5 \ge 0\) || \(5 \le 6\) Both statements are true, so Condition A is true.

Check Condition B:

Condition B: \(z - y > y\) Substitute the given values: \(8 - 6 > 6\) Simplify: \(2 > 6\), which is false. Therefore, Condition B is false.

Check Condition C:

Condition C: \((z - y > x)\) Substitute the given values: \((8 - 6 > 5)\) Simplify: \((2 > 5)\), which is false. Therefore, Condition C is false. So the final verdict for each condition is: A) True B) False C) False

Key concepts

Conditional Operators

Understanding conditional operators is essential for decision-making in programming. In C++, conditional operators evaluate a statement and return a boolean value accordingly. The most commonly used operators are the comparison operators such as '==' (equal to), '!=' (not equal to), '>' (greater than), '<' (less than), '>=' (greater than or equal to), and '<=' (less than or equal to).

Let's consider condition A from the exercise, which uses '>=' and '<='. We assess if one variable is greater than or equal to another, or one is less than or equal to another. In this exercise, checking if '5 >= 0' or if '5 <= 6' both statements are individually evaluated and found to be true. Since just one of the conditions needs to be true for the whole expression to be true (due to the OR operator), the final result for Condition A is true. Conditional operators are thus foundational in constructing meaningful control flow in your programs.

Boolean Expressions

Boolean expressions evaluate to either true or false and are pivotal in conditional statements such as 'if', 'while', or 'for'. They are built using boolean logic, which involves constants true and false, and the data type 'bool' in C++. In the context of our exercise, the conditions given (A, B, C) are all boolean expressions that are evaluated with the help of logical and conditional operators.

For instance, when evaluating condition B ('z-y > y'), substituting the values results in '2 > 6'. Since this statement is not true, the boolean expression evaluates to false. It's crucial to understand that boolean expressions are the core of decision-making logic in programming and knowing how to construct and evaluate them is a highly valued skill in computer science.

Logical Operators

Logical operators in C++ are used to combine multiple boolean expressions. The three primary logical operators are AND ('&&'), OR ('||'), and NOT ('!'). They operate on boolean values and produce boolean results.

In our exercise condition A, we encounter the OR operator '||'. This operator returns true if either of the operands is true. Therefore in condition A, even if just one of '5 >= 0' or '5 <= 6' is true (in this case, both are), the entire expression will evaluate to true. The AND operator, on the other hand, would require both operands to be true for it to return true, which is important to remember when constructing more complex boolean expressions. Recognizing and utilizing logical operators correctly is fundamental in creating sophisticated logical conditions in your code.