I am definitely missing something in this relation

[nistaria]

Homework Statement

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

Homework Equations

c)x=1

The Attempt at a Solution

According to class notes I took, as this simple question was solved in class
Reflexive: no (2,2) is not in the relation
Symmetric: no if(1,2)$$\in$$R(relation,not real number) but (2,1)$$\notin$$R
Anti-symmetric: yes
let (x,y)$$\in$$R
===>x=1
if y$$\neq$$x, then y$$\neq$$1 and (y,x)$$\notin$$R since y$$\neq$$x=1

Transitive?
Yes
let (x,y)$$\in$$R and (y,z)$$\in$$R
===> x=1 and y=1
===> (x,z)$$\in$$R

My question is .. how is it possible that it is not reflexive transitive, symmetric or for that matter is anti-symmetric?
How is it possible that y does exists in the relation? Wouldn't that be a false value to begin with? As in if we have a false value then we cannot compare it to the existing relation?

 

[nistaria]

Alright well I just figured it out.. i really need to stop pulling these all nighters and my only source of nutrition being candy bars and coffee.
The answer is so obvious and I definitely didn't see it.