The answer could be A depending upon the interpretation of the problem.
In another interpretation of the problem, the answer could be (C).
I just took the set like {-3, 0 3}
I looked at statement (1)
-3 + 3 = 0 is in the set
0 + 3 is in the set
3 + 3 should be there as well, so set should be {-3, 0 , 3 , 6}
So you could go ad infinitum to show that the set is really {-3, 0, 3, 6, ...+infinity}
Sufficient
Then I looked at statement 2, Again started with {-3,0,3} backwards
3 - 3 = 0 is in the set
0 - 3 = -3 is in the set
-3 - 3 = -6 should also be there, so set should be {-6, -3, 0, 3}
So you could go ad infinitum to show that the set is really {-infinity, ...-3, 0, 3}
OK, so Statement 2 tells me that all positive multiples of 3 are not in P, UNLESS P already has ALL positive multiples of 3. That is, a situation like
{-infinity, ..., -3, 0, 3, 6, ....+infinity}
If that were not the case, I could argue that Statement 2 is ALSO SUFFICIENT TO TELL ME THAT THE SET WOULD NOT CONTAIN ALL +VE MULTIPLES OF 3. In this interpretation, Statement (2) is also SUFFICIENT.
But given that "infinity" itself is an ethereal concept, take your pick!
Rehana
