The equation of straight lines l1 and l2 are see the photo

Very interesting and inspiring problem.  Wish there are more of these.

First, we know that a possible equation of L2 is  y=1, then c=-1 => -y=-1 or y=1.
Of course, c could be just any negative number so that L2 lies above the x-axis.
=> c<0 (III)  is true

Next, we note that L1 has a negative intercept, that meant that when x=0, y<0.  Go back to the original equation
ax+by=-1 => when x=0, by=-1, so b>0 in order for y to be negative.  So
b>0.   
We already know that c<0, so
b>c (II)  is true

Further, we note that L2 has a negative slope.  From the definition of slope, m, where m=-a/b 
=>
m=-a/b<0 => a/b>0.
We already know that b>0, so for a/b>0, a>0.  Therefore
a>0  (I)  is true

So we have established the truth values of (I), (II) and (III).
It will be up to you to select the answer choices.

Do check and understand all the arguments.  If in doubt, please post your queries.