An example for explanation for a true statement in problem:

  What we want to do to show that the statement is true is
  to show there's a y (in the positive integers) to satisfy 
  any value of x (which has a domain of all integers)

  ex:

    Ax Ey (y = |x| + 1)

  The statement is true since 
    when x is positive or 0, y is that positive value or 0 + 1, 
      which remains positive
    when x is negative, y is simply 1 + the corresponding 
      positive value of the absolute value of x, which is
      also positive

For other problems, the explanation might be much simpler, e.g.,

  when x = 10, the statment is true for all values of y