I'm currently doing work on discrete mathematics in my free time and am having some difficulties with understanding some questions pertaining to Relations and Functions. To be specific, I'm stuck on the following practice question:
We have a relation $R$ on $\mathbb{Z}+$ defined as follows: $mRn$ if and only if $m|n$, with $A = \{ 1,2,4,13,26,52 \}$
Determine the set $B = \{n ∈ \mathbb{Z} \ | \ 52Rn \}$.
Indicate whether $A \cap B = \varnothing$.
Would the answer to (1) just be all integers that are divisible by 52?
As for (2) I'm unable to answer because I do not have the set $B$.
Any help is greatly appreciated!
Thank you.
a) Note it is 52Rn, and not nR52. So it would be all the integers that 52 divides into. In other words all the multiples of 52.
b) A intersect B = all the multiples of 52 in A. Which is {52}. So it isn't empty.