Math question on propostions?

Question

The propositions below can be arranged in three groups so that each member of a group is logically equivalent to the other two. Find the three groups
1) If the system is not ready then the light is not on.
2) If the light is on then the system is not ready.
3) If the light is not on then the system is not ready
4) If the system is ready then the light is on.
5) Either the system is not ready or the light is not on.
6) Either the system is not ready or the light is on.
7) Either the light is not on or the system is ready.
8) If the system is ready then the light is not on.
9) If the light is on then the system is ready.
GIve your answer by listing the three groups, for example "2,5and9"

Answer 1

{1, 7, 9}, {2, 5, 8}, {3, 4, 6}

Basically, this is based on being able to recognize the equivalence of P→Q, ¬Q→¬P, and Q∨¬P. Consider just the first group -- 1 states that if the system is not ready, the light is not on. So if the light is on, then that means the system must be ready, which is what 9 says (this is the equivalence of P→Q and ¬Q→¬P). Also, if 1 holds, then there are two possibilities -- either the system is ready or it isn't, and if it isn't then the light isn't on, so either the system is ready or the light is not on, which is what 7 says. The reverse implications also hold -- that is, 7 also implies 1 and 9 also implies 1. The other two groups are decided in much the same way.