Sets

[email protected] wrote:appologies it was meant to read

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 the integer are also in P

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

The answer should be A. We want to know if P contains all the positive multiples of 3- that is, we want to know if all of the numbers 3, 6, 9, 12, 15, etc... are in P. Assume 1) is true: if x is in P, then x+3 is in P. We know 3 is in P. So 3+3 = 6 is in P. And if 6 is in P, then 6+3 = 9 is in P. And so on- every positive multiple of 3 must be in P.

Statement 2) is not sufficient. We only know that 3 is in P. From 2), we know that 3-3 = 0 is in P, and thus that 0-3 = -3 is in P, and so on. From 2) we would know that every negative multiple of 3 is in P, but we don't know enough to conclude that any positive multiple of 3 is in P, with the exception of 3 itself.