Relation that is 1-1, reflexive, but not symmetric

Lets say a set A has seven elements . Can a relation on A be 1-1, reflexive, but not symmetric?

I say no its impossible cause in order to be not symmetric and reflexive we would have to use an element in the domain more than once and that would not make it 1-1.

What do you think?

Re: Relation that is 1-1, reflexive, but not symmetric

If $\displaystyle R\subset A\times A$ is reflexive, then $\displaystyle (a,a)\in R$ for all $\displaystyle a\in A$ . If $\displaystyle R$ is one to one, then $\displaystyle (a,b)\in R$ and $\displaystyle (a,c)\in R$ implies $\displaystyle b=c$ that is, necessarily $\displaystyle R=\Delta=\{(a,a):a\in A\}$ . This means that $\displaystyle R$ is the equality relation on $\displaystyle A$ (equivalence relation).

Re: Relation that is 1-1, reflexive, but not symmetric

Re: Relation that is 1-1, reflexive, but not symmetric

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**Aquameatwad** So no?

Yes, no.