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: $$7<=x \& \& \quad z>4$$

Short answer

$$7\le x \quad \& \& \quad z>4$$ Answer: False

Step-by-step solution

Substitute the values of x and z

We are given x=5, and z=8. Replace x and z in the given condition with their respective values: $$7\le5 \quad \& \& \quad 8>4$$

Evaluate the inequalities

Evaluate both inequalities separately: $$7\le5\ \text{is False}\\ 8>4\ \text{is True}$$

Evaluate the logical AND

Evaluate the logical AND operator (&&) using the truth values of the inequalities from Step 2: False AND True = False So, the answer is False.

Key concepts

Conditional Expressions

In programming, conditional expressions are at the heart of decision-making. Simply put, they help determine which code block should be executed based on certain conditions. The basic format involves evaluating an expression to return a boolean value—either true (non-zero) or false (zero).

For example, in C++, we might have a conditional expression like if(a > b), where a and b are variables. The condition inside the parentheses is checked: if a is indeed greater than b, the expression evaluates to true and the subsequent code block is executed. Conversely, if the condition is not met, the expression evaluates to false, and the program may run alternative code or skip the block entirely.

Conditional expressions can get complex with the presence of logical operators such as AND, OR, and NOT which allow combining multiple boolean expressions into one. Understanding how to construct and evaluate these expressions is critical for creating effective and efficient programs.

AND Operator

The AND operator, denoted by && in C++, is a fundamental logical connector that joins two boolean expressions. For the resulting condition to be true, both operands must be true. If either of the operands is false, the whole expression evaluates to false.

In the context of the given exercise, the AND operator is used between two inequalities. Both conditions on either side of the && must hold true for the statement 7 <= x && z > 4 to return true. This evaluation is quite similar to a dual switch where both switches must be 'on' for the circuit to complete. Logical operators like AND are crucial in scenarios where multiple criteria must be met before an action is executed.

The correct use of logical operators allows programmers to handle decisions efficiently within a program, though one must be cautious. Inelegant or incorrect use might lead to complex code that is hard to debug and maintain.

Inequality Evaluation

Inequality evaluation in C++ involves comparing two values and determining whether the comparison statement is true or false. The comparison operators used for this purpose are <, >, <=, and >=. These operators are read as 'less than', 'greater than', 'less than or equal to', and 'greater than or equal to', respectively.

As observed in the exercise, individual inequalities like 7 <= 5 and 8 > 4 are assessed before being combined with a logical operator. It's essential first to understand these simple evaluations before advancing to more complex logical expressions. In case of 7 <= 5, the statement is false because 7 is not less than or equal to 5. Conversely, 8 > 4 is true since 8 is indeed greater than 4. It's worth noting that proper evaluation of inequalities is key when programming algorithms involving sorting, searching, and decision trees, where the correct comparison can determine the entire algorithm's path.