im working on the practice problem on unit about sets and relations The question is: Let a = {1,2,3,4} and R be a binary relation on A x A given by: ((a,b),(c,d)) ∈R if and only if a divides c and b divides d. Draw its diagram.
Im having a trouble figuring how to draw the diagram because I was never taught how to draw it.. I assume that I should start with (1,1) at the most bottom and place (1,2),(1,3),(1,4) above it and so on.
Little help will be very much appreciated Thank you!
Well, you have a set with 16 elements, so you need to draw 16 points on the plane and join some of them with arcs. The trick is not to draw too many arcs - for example, you'll need to draw an arc between (1, 1) and (1, 2) and another arc between (1, 2) and (2, 2), but you shouldn't draw an arc between (1, 1) and (2, 2) because of transitivity (which I think you'll need to prove):
$$(1, 1) \le (1, 2) \le (2, 2)$$
So, the total number of arcs won't be too many, and your drawing will be quite understandable.