So I get the basics of these four topics (reflexive, symmetric, antisymmetric, and transitive). I understand the rules in which they work but for some I am having a hard time figuring out what exactly this question is asking.
Determine whether the relation R on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x,y) is an element of R if and only if:
A) x + y = 0
B) x = + or - y
C) x - y is a rational number.
D) xy = 0
And so forth.
So is the question asking if the elements of R are only elements if (for the case of D) ) they satisfy the condition of xy = 0. So if that is the case, (1,1) would not be in my set and is not taken into consideration in answering the 4 questions?
Okay so re reading what I just typed can be confusing so I am going to post one of my answers.
For A) I have:
Reflexive: No: Counter example: (1,1) is an element of R but 1 + 1 does not equal 0. Therefore, it cannot be reflexive.
Now I am not sure if (1,1) can actually be taken into consideration because to satisfy the condition of x + y = 0, the point (1,1) would not be used.
I have a feeling I am over thinking the problem but this is frustrating me beyond control. Thanks for the response!