Question 3. (9 points) We defined the set N CR of natural numbers. The set Z of integers is defined as Z=-NU {0} UN where -N := {n ER| -n E N). In the following you may assume that N is closed under addition and multiplication. 1. Show that Z is closed under addition and multiplication: the sum and product of two integers is again an integer. 2. Show that for all integers n, -n is also an integer. 3. Show that unless n = 1, there is no integer n such that n- Z.