T = {all elements here are sequence of positive integers}
Given that A superset must contain finite (or known) numbers of multiple of three.
Question=> Is T a superset?
i.e. does T contains a finite/known element which are multiples of three?
Statement 1: The first six integers in T are multiples of three.
This implies that set T contains more than 6 elements of set T.
If the remaining elements in set T include multiples of three, then it will be difficult to ascertain the numbers of multiples of three in set T. But if the remaining elements in set T do not include multiples of three, then set T contains a finite/known numbers of three.
Despite this, the information provided in statement 1 does not prove
(-) Whether the elements in set T are finite or Not.
(-) Whether all elements in set T are multiples of three or not.
Therefore, statement 1 is not sufficient.
Statement 2: An infinite number of integers in T are multiples of four.
This implies that the elements in set T are either multiple of four or multiple of three and four. If they are multiples of four alone, then the number of multiples of three in set T can be deciphered to be zero (0). However, if the elements in set T are multiples of three and four, then the number of multiples of three in set T cannot be determined. Hence, statement 2 is NOT SUFFICIENT.
Combining both statements together:
We can draw up the following conclusion;
(-) Set T contains an infinite number of positive integers which are multiples of four.
(-) The first six integers are multiples of three.
(-) The first six integers must be multiple of three and four.
If it is only the first six digits that are multiple of three, then we have, known number of multiples of three.
If the remaining element in set T (aside from the first 6 digits) are multiples of three as well then we have infinite number of multiple of three.
Hence both statements combined together are NOT SUFFICIENT.
Answer = option E
