Question 1

(1) 
   (a) true for all non-negative values of x
   (b) true for all non-negative values of x
(2)
   (a) error when x = 0; true when x > 0
   (b) true for all non-negative values of x

Question 2

The result is true for all values of x

Question 3

(1) all integers
(2) x >= 0
(3) x <= 0

Question 4

{(x,int), (y,int)}
{(x,int), (y,real)}
{(x,real), (y,int)}
{(x,real), (y,real)}

Question 5.

Note: The repeat-until in this question is different from the one
you learned in PASCAL or other programming languages. The repeat-until 
presented here quits after the condition becomes false (same as
do-while in C/C++).

1. repeat Stm until Exp
   can be defined as

    Stm; 
    while Exp do Stm

2. while Exp do Stm
   can be defined as

    if Exp then 
      repeat Stm until Exp 
    else 
      skip

If we use the "other meaning" for repeat-until, the solution should
look like:

1. repeat Stm until Exp
   can be defined as

    Stm; 
    while (not Exp) do Stm


2. while Exp do Stm
   can be defined as

    if Exp then 
      repeat Stm until (not Exp)
    else 
      skip