(4) Using the basic rules BR1 - BR12, show that the following property of real numbers holds:
SOLUTION:If a < 0 and b > c, then ab < ac.
NOTE: In this solution we have suspended some details that you might want to fill in. For example, we have used the fact that (-a)(-c) = ac which technically needs to be proven using the basic rules. One always has to make choices on how much detail to show. In mathematics, we usually show enough detail so that the key ideas of an argument are clear.a < 0 and b > c implies -a > 0 and b - c > 0 which implies (-a)( b - c ) > 0 BR-12 which implies -ab + ac > 0 which implies ac - ab > 0 which implies ab < ac.