For each of the following relations on the set of all real numbers, say whether it is reflexive, symmetric, anti-symmetric, and transitive.

Question

I am confused about this question : x=1. How can we solve this? Do we assume that R = { (x,y)| x=1 }. Do we just add the "y" variable? Since I do not know how to solve a relation with just one x variable. Pleas Help.

Thanks.

Answer 1

Yes, it is most likely implicit in the question that "$x=1$" means the relation $R=\{(x,y)|\hbox{$y$ is a real number and}\ \ x=1\}$. Can you proceed from here?