Ordered Pairs in Relation A to B

[bird34]

Homework Statement

List the ordered pairs in the relation R from A = {1, 2, 3, 5} to B = {2, 4, 6, 9} where <x, y> is an element of R iff:

(i) x ≥ y
(ii) x – y < 2
(iii) x – y > 2
(iv) l.c.m. (x, y) = 18
(v) g.c.d. (x, y) = 3


I understand in general ordered pairs and cartesian products, but I'm not sure where to begin when there are limitations such as these.

 

[tiny-tim]

welcome to pf!

hi bird34! welcome to pf!

(you understand they're alternatives?)

what's the difficulty?

eg for (ii), R = {(5,9),(5,6),(5,4)…}

 

[bird34]

I guess maybe I don't understand after all. I get where the numbers came from for (ii), but what about the others ones? I'm lost and need an explanation. Thanks!

 

[tiny-tim]

for (ii), R is the set of all ordered pairs (x,y) such that x - y < 2

so eg 5 - 4 < 2, so (5,4) is in

but 5 - 2 =3, so (5,2) is out

 

[bird34]

Ok, so for (iii), the answer would only be {5,2}?

 

[bird34]

And for (i) it would be R = {2,2}, {3,2}, {5,2}, {5,4}?

If so, I feel like an idiot for overlooking the simplicity in this!
By the way, do you know anything about a digraph?

 

[tiny-tim]

And for (i) it would be R = {2,2}, {3,2}, {5,2}, {5,4}?

yup!

By the way, do you know anything about a digraph?

no, we never did them

Ok, so for (iii), the answer would only be {5,2}?

well, that's the only one with x = 5