Transitive Closure of Relations on S: Solutions

[dcramps]

Homework Statement

Let S = {1, 2, 3, 4}. For each of the following relationson S give its transitive
closure.

(a) {(1, 1), (3, 4)}
(b) {(1, 2), (4, 4), (2, 1), (4, 3), (2, 3)}
(c) {(1, 1), (2, 2), (3, 3), (4, 4), (4, 1)}
(d) {(1, 3), (3, 2), (2, 4), (4, 1)}

Homework Equations

N/A?

The Attempt at a Solution

I honestly have absolutely no idea what I am supposed to be doing. Any push in the right direction would be appreciated. Not asking for an answer here.

 

[Mark44]

What's the definition of transitive closure for a relation?

 

[dcramps]

I have absolutely no idea. I got some help from a classmate and I think I have it somewhat figured out?

for a, there is none
for b, I found (1,1) (2,2) and (1,3)
for c, there is also none since anything you can find is already there..
d still working on.

Just wondering now how do I format this into an answer? Do I just do {(1,1),(2,2),(1,3)} and so on?

 

[Mark44]

How can you give the transitive closure of a relation without knowing what it is?