.
Multiples of 12 are a subset of the multiples of n
What must be true about n?
a- 12<= n
b- n<= 12
c- 12|n
d- n|12
e- n and 12 are relative prime.
I think n<=12 , and n|12
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this problem, we have two subsets of integer numbers.
One subset, let's call it T, is the subset of multiples of 12: T = {12, 24, 36, . . . }.
Another subset, let's call it N, is the subset of multiples of n: N = {n, 2n, 3n, . . . }.
We are given that T is subset of N, or, in other words, every number of T, i.e. a number
of the form 12k, is the element of N: 12k = m*n for some m.
In particular, the number of 12 is the element of T, i.e. 12 = m*n for some integer m.
It means that n is a divisor of 12, or n|12.
ANSWER. Both conditions, (b) and (d), must be satisfied.
Solved and explained.
