Question

We have a relation R on Z+ defined as follows: mRn if and only if m|n.

a. Explain why the relation R is not a function.
b. Determine the set A = {m ∈ Z|mR52} and give its cardinality |A|.
c. Determine the set B = {n ∈ Z|52Rn}.
d. Indicate whether A ∩ B = ∅.

Answer 1

(a) clearly 2R4 and 2R6. for a function, the each m must be related to a single n

(b) A is the set of factors of 52. I'm sure you can list them.

(c) B is the set of all multiples of 52.

(d) A ∩ B = {52}