If a, b, c are integers and ab>0, bc >0, ac<0, then which of the following must be true?
I.	a>0, b>0, c>0
II.	a=0, b=0, c=0
III.	a<0, b<0, c<0
Choose the correct choice.
A) I only	B) II only	C) III only	D) I, II and III	E) None of the above
We could solve this easily using counter examples.   I is false. If a&gt;0 and c&gt;0, then ac&gt;0. But since ac&lt;0, it is false.   II is false. If a=0 or b=0 or c=0 then ab=bc=ac=0.   III is false. If a&lt;0 and c&lt;0, then ac&gt;0. But since ac&lt;0, it is false   So, the answer is None of the above
<result>E</result>
If a, b, c are integers and ab>0, bc >0, ac<0, then which of the following must be true?
I.	a>0, b>0, c>0
II.	a=0, b=0, c=0
III.	a<0, b<0, c<0