I will be glad to give you the answers to three of these as representatives of the others.
BUT, I will not give them with explanations. I expect you to puzzle out the reasons.
Then you should respond with the solutions to the others.
I am confused on what to do with this problem from my textbook because it does not give me sets. For example: A = {1, 2, 3} and B = {1, 2, 3, 4} and R1 = {(1,1), (2,2), (3,3), (4,4)} and R2 = {(1,1), (1,2), (1,3, (1,4)}, then I can do the unions and intersection, etc but I do not have that options here.
What I have is this as my problem:
R1 = {(a, b) R^2 | a > b}, the "greater than" relation
R2 = {(a, b) R^2 | a > b}, the "greater than or equal to" relation
R3 = {(a, b) R^2 | a < b}, the "less than" relation
R4 = {(a, b) R^2 | a < b}, the "less than or equal to" relation
R5 = {(a, b) R^2 | a = b}, the "equal to" relation
R6 = {(a, b) R^2 | a b}, the "equal to" relation
Find:
a.) R1 U R3
b.) R1 U R5
c.) R2 R4
d.) R3 R5
e.) R1 - R2
f.) R2 - R1
g.) R1 R3
h.) R2 R4
The R1, R2, R3... the numbers are subscripts.
Also If I have this, what do I do if i have this white circle in between them, not up high. For example:
a.) R1 R1
I have 5 problems similar to this one.
We have not done any Trichotomy property. We did Transitive, Symmetry, Antisymmetry, Reflective, and Irreflective. Thats what we covered and this problem is part of the exercise in this chapter.
Well I will see what I can do with the other problem and run it by you to see if I am doing this correct.