Let $A = \{1,2\}$ and $R = \{(1,1)\}$. Is $R$ reflexive on $A$?

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Assume we have $A = \{1,2\}$ Suppose $R$ is relation on $A$

Case 1

Let $R = \{(1,1),(2,2)\}$

I suppose in this case $R$ is reflexive.

Case 2.

Let $R = \{(1,1)\}$

Definition of the reflexive relation from the book:

If $R$ is a relation on A and $\forall x \in A(xRx)$, then $R$ is reflexive.

Looking at this definition, I believe that in case 2 $R$ is not reflexive, but I am not sure. Is it?