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Chapter 3: Problem 3

In college algebra we see numeric intervals given as $$2 < x < 3$$ In \(\mathrm{C}_{++}\) this interval does not have the meaning you may expect. Explain and give the correct \(\mathrm{C}_{++}\) Boolean expression that specifies that \(\times\) lies between 2 and 3

Short Answer

Expert verified
Question: Explain the given numeric interval "\(2 < x < 3\)" and its meaning in the C++ programming language. Answer: The given numeric interval "\(2 < x < 3\)" means that the variable x should be greater than 2 and less than 3. In C++ programming, this interval can be represented as a Boolean expression: `(x > 2) && (x < 3)`. This expression will return true if x lies between 2 and 3 (excluding 2 and 3).

Step by step solution

01

Understanding the given numeric interval

The given numeric interval "\(2 < x < 3\)" represents a range where the variable x lies between 2 and 3, but does not include the values 2 and 3.
02

Explain the meaning in C++

In the C++ programming language, we can't directly use the given interval as-is. Instead, we need to combine two comparison operators with a logical operator. We'll have to compare x with 2 and 3 separately, and then combine the comparisons using a logical operator like "AND" for the desired output.
03

Writing the correct C++ Boolean expression

To express the given interval in a C++ Boolean expression, we'll write: ```cpp (x > 2) && (x < 3) ``` This expression states that `x` should be greater than 2 AND `x` should be less than 3, which satisfies the given numeric interval condition. Whenever x lies between 2 and 3, this C++ Boolean expression will return true.

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