sets!!

[Ozlemg]

Set T is an infinite sequence of positive integers. A "superset" is a sequence in which there is a finite number of multiples of three. Is T a superset?
(1) The first six integers in T are multiples of three.
(2) An infinite number of integers in T are multiples of four.

[kevincanspain]

(1) We know that the number of multiples of 3 in T is at least 6, . However, we cannot establish an upper bound on the number of multiples of 3 in T NOT SUFF
(2) says nothing about the number of multiples of 3 in T, as it is possible that there is a infinite number of multiples of 3 in T. For example, if T were the set of all positive integers, T would have an infinite number of multiples of k (k could be any positive integer)
(T) Nothing in the two statments implies or precudes the existence of an infinite number of multiples of 3

For example: (3,6,9,12,15,18,4,3,8,6,12,9,16,12,20,15,...)

AND (3,6,9,12,15,18,4,8,4,8,4,8,4,8,4,...)

[krishnasty]

IMO E

The first statement produces no finite result on multiples of T. Hence, not sufficient.
The second statement says about multiples of 4 but we are looking for multiple of 3'

Combined, again, there is no finite reult of multiples of 3 in the set T.

Whats the OA?

[Sanjay2706]

So here, because we can't assume that the first statement means that there would be finite nos . I would go for E