3) is the easiest case. and are contradictory. Thus .
So consider case 1):
We know that and a is positive, so . This means that either both b, c are positive or both b, c are negative.
If both b, c are positive then is trivial since the RHS is negative, and we have no contradiction.
If both b, c are negative then
Now if then
is a contradiction because and the RHS is negative.
If and we know that c is negative then cannot be true because , a contradiction.
Thus we are left with .
Thus both b and c cannot be negative.
Thus case 1) says that if a is positive, so are both b and c.
Case 2) works in a similar fashion to show that, at best, all three of a, b, and c must be negative. (I leave this for you to show.) This again contradicts .