2 different Set Relations. I need to come up with a rule for each Relation.
R1 = {(a,b) ∈ A x A : rule} where A = {1, 2, 3, 4, 6, 12}
I know that they're all positive integer and are divisors of 12.
How could I create a rule for this? Would it be something like R1= {(a,b) ∈ A x A : a|b }
Relation 2 R2 = {(a, b) ∈ B x B : rule} where B = {1, 2, 3, 4, 5}
Would the rule for this relation be R2 = {(a, b) ∈ B x B : a ≥ 1 and b ≤ 5 } or maybe R2 = {(a, b) ∈ B x B : x ∈ N, 1 ≤ x ≤ 5 }
If it helps to make more sense I was given directed graphs for each relation:
Relation 1 had a directed graph showing the relation as (1, 2), (1, 3), (1, 4), (1, 6), (1, 12), (2, 4), (2, 6), (2, 12), (3, 6), (3, 12), (4, 12), (6, 12)
Relation 2 had a directed graph show the relation as (1, 2), (1, 3), (2, 3), (2, 4), (3, 4), (3, 5), (4, 5)
Any help or a link you think would explain creating rules would be greatly appreciated.
As user247327 says, your first relation looks like $\{(a,b) \in A \times A : a < b \text{ and } a|b\}$. This is the set of pairs $(a,b) \in A \times A$ where $a$ is less than $b$ and $a$ evenly divides $b$.
Your second relation looks like $\{(a,b) \in B \times B : b-a \in \{1,2\}\}$. This is the set of pairs $(a,b) \in B \times B$ where the $a$ and $b$ are not equal and at most $2$ apart (and $a$ is less than $b$)