Data Sufficiency question

mgroeber wrote:IF P is a set of integers and 3 is in P, is every positive multiple of 3 in P?

1) For any integer in P, the sum of 3 and that integer is also in P.

2) For any integer in P, that integer minus 3 is also in P.

1 is sufficient. Please explain. I thought 2 is sufficient as well.

Thanks!

positive multiple of 3 are 3,6,9,12 .......

as 3 is in P 1) is sufficient to prove that 6 is there , 6+3=9 is there etc etc ... So 1) is sufficient

Now as per 2)
3 is in P
so 0 should be in P , so as -3,-6,-9 ...etc
It is not sufficient to prove that all positive multiples are in P (although it is sufficient to show all -ve multiples of 3 are in P)

So 2) is not sufficient