Please help me with this question. Mostly, I am not understanding the 6n:n ? Z+

Question

Please help me with this question. Mostly, I am not understanding the 6n:n ? Z+ or the 3n:n ? Z+

I know that D is a set of multiples of 3 (3, 3+3=6, 3+6=9, etc.) and I know that 6n is a partial function of n(positive integer) which is a proper set D. I dont know how to determine the answer though. Any help will be apriciated and best answer gets the points =)

Let D be the set whose members are defined as follows. Basis Step: the number 3 D. Recursive Step: if x D and y D, then x + y D. Determine if {6n: n Z+} D and proves your answer (10 pts. ). Determine if D {3n: n Z+ } and proves your answer (0 pts. ).

Explanation / Answer

D is a set of multiples of 3. Any number of the form 6n can ber written as 3*(2n) which is a multiple of 3. So every number in the 6n set is in D. This implies that 6n is a subset of D.

D is a set of multiples of 3. {3n:n ? Z+} is the exact same set. Equal sets are subsets of each other. Hence D is a subset of 3n:n ? Z+

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