Chapter 55 Problem 6E from Discrete Mathematics and Its Appl

Chapter 5.5, Problem 6E from

Discrete Mathematics and Its Applications 7^th Edition by Rosen, Kenneth

Problem

Use the rule of inference developed in Exercise 5 to verify that the program

if x<0 then

y : = 2|x|/x

else if x > 0 then

y : = 2|x|/x

else if x = 0 then

y : =2

is correct with respect to the initial assertion T and the final assertion y = 2.

Solution

If the intiial assertion is true, and x<0 , then after the if-body y will be 2.

If the initial assertin is true but x>0 is true, then after the else-body, y will be -2

So using the rule of inference , we get this segment is true with respect to the final assertion.