bupbebeo wrote:IF P is a set of integer and # 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 , that integer minus 3 is also in P
Statement (1)
Suppose x = integer in set P .
Then x + 3 is in P .
Now x + 3 may be a multiple of 3 may not be .
Not sufficient .
Statement (2)
Suppose x = integer in set P .
Then x - 3 is in P .
Now x - 3 may be a multiple of 3 may not be .
Not sufficient .
Combine (1) and (2)
Now if you take any multiple of 3 and add or subtract 3 from it you will always get a multiple of 3 .
That is = > x (mul of 3)+/- 3 = y (mul of 3) . Y = integer .
This is in fact true for any integer
x (mul of A)+/- A = y (mul of A)
Here x , y and A are all integers .
Set P consists entirely of multiples of 3 only .
Ans C