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Chapter 5: Problem 16

Give a precondition and a postcondition for the predefined function sqrt, which returns the square root of its argument.

Short Answer

Expert verified
Answer: The precondition for the sqrt function is that the input argument must be a non-negative number (x ≥ 0). The postcondition is that the output (result) is always a non-negative number, and it is the correct square root of the input argument (y ≥ 0 and y² = x).

Step by step solution

01

Precondition for sqrt

The precondition for the square root function is that the input argument must be a non-negative number (i.e., a positive number or zero). In other words, the input number should not be a negative number. This is essential because the square root of a negative number is undefined in the real number system. Mathematically, the precondition can be represented as: \[ x \geq 0 \]
02

Postcondition for sqrt

The postcondition for the square root function is that the output (result) is always a non-negative number, and it is the correct square root of the input argument. This means that when the output is squared, it should be equal to the input argument. Mathematically, the postcondition can be represented as: \[ \sqrt{x} = y \Rightarrow y \geq 0 \text{ and } y^2 = x \]

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