I have a question that I got wrong in my homework and I am having trouble understanding.
It says "Determine whether the relation R on the set of all real numbers is reflexive, sym- metric, antisymmetric, and/or transitive, where (x, y) ∈ R if and only if"
One of these are x=1.
This means the relation looks like this:
1,1 1,2 1,3 1,4
and so on. That means that X will never not be one. I determine this as reflexive because every x has a matching y, such as 1,1. However, if every Y also has to have a matching X, then I am wrong.
Is my latter guess correct? Does reflexive mean if x,y, every x must have a matching x,x or does it also apply that every y must have a y,y.
Reflexive means that for every $t$, $(t,t)$ is in the relation. The relation $x=1$ is not reflexive as $(2,2)$ is not in the relation.