Assignment:
Q1. Consider the set of integers Z. The set Z x Z consists of all ordered pairs of integers. In symbols,
ZxZ={(x,y):x,y∈Z}
For example, (2,-5) , (0,0) , (-127,10) , and (-5,2) are all distinct elements of Z x Z.
Notice that the order matters; (2,-5) and (-5,2) are different elements of Z x Z.
Now let’s define a few functions on Zx Z:
f(x,y)=x*y
g(x,y)=max?{x,y}
h(x,y)=x^y
(a) What is the range of each of these functions? In other words, is the image an integer, a rational number or only a real number?
(b) For which of these functions (if any) is the image of (x,y) equal to the image of (y,x)?
Provide complete and step by step solution for the question and show calculations and use formulas.