Quantitative

Guys, I do need your explanations why the correct answer of this question is C

If the quotient a/b is less than zero, which of the following cannot be true?
A. a > 0
B. b > 0
C. ab > 0
D. a-b > 0
E. a+b > 0


As we know that if a is positive, b must be negative, vice versa.
Answer choices
A. If A can be negative , so it cannot be true that A > 0
B. It's same as the answer choice A
C. If A is positive and B is negative , it cannot be greater than 0
D. If A is -4 and B is 2, cannot be greater than 0
E. E is like D