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

**Aquameatwad** · November 15th 2011, 05:04 PM

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?

**FernandoRevilla** · November 15th 2011, 09:13 PM

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

**Aquameatwad** · November 16th 2011, 12:03 PM

So no?

**FernandoRevilla** · November 16th 2011, 01:13 PM

Originally Posted by Aquameatwad

So no?

Yes, no.

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