Question

which of the following is the correct boolean expression to test for: int x being a value between, but not including, 500 and 650, or int y not equal to 1000?

○ ((x >= 500 && x <= 650) && (y != 1000))

○ ((x > 500 and x < 650) or!(y.equal(1000)))

○ ((x > 500 && x < 650) || (y != 1000))

○ ((x < 500 && x > 650) ||!(y == 1000))

Explanation:

Step1: Analyze the condition for x

The problem states that x should be between, but not including, 500 and 650. So the correct condition for x is \( x > 500 \) and \( x < 650 \), which in Java (or similar languages) is written as \( x > 500 \&\& x < 650 \).

Step2: Analyze the condition for y

The condition for y is that it is not equal to 1000. In Java, the not - equal operator is !=, so the condition for y is \( y != 1000 \).

Step3: Analyze the logical operator between the two conditions

The problem says "or" between the two conditions (x in the range or y not equal to 1000). In Java, the logical OR operator is ||.

Now let's analyze each option:

• Option 1: \( ((x >= 500 \&\& x <= 650) \&\& (y != 1000)) \): This uses AND (&&) between the x condition (which includes 500 and 650) and y condition, which is incorrect.
• Option 2: \( ((x > 500 \text{ AND } x < 650) \text{ OR }!(y.equal(1000))) \): First, in Java, we don't use AND (we use &&), and also for an int variable y, we don't use the equal method (we use != for not - equal comparison). So this is incorrect.
• Option 3: \( ((x > 500 \&\& x < 650) || (y != 1000)) \): This has the correct condition for x (between 500 and 650, not including), the correct condition for y (not equal to 1000), and the correct logical OR (||) between them.
• Option 4: \( ((x < 500 \&\& x > 650) ||!(y == 1000)) \): The condition for x (\( x < 500 \&\& x > 650 \)) is always false, so this is incorrect.

Answer:

\( ((x > 500 \&\& x < 650) || (y != 1000)) \) (the third option)