How to construct relations on the following domain?

Question

Construct the following relations on the domain {1,2,3}.

A relation that is transitive and symmetric, but not reflexive or antisymmetric.

How would I construct the above relation?

I have attempted similar problems with the two being below.

Note that your example about a relation that is both symmetric and anti-symmetric is wrong. Why? — Santana Afton, Commented Mar 26, 2019 at 4:24
Would this be correct for the relation with symmetric and anti-symmetric? {(1,2),(2,1),(2,3)} — Anonymous, Commented Mar 26, 2019 at 4:56
To be antisymmetric, it must be that if $(1,2)$ is in the relation, then you cannot have $(2,1)$ in the relation. — Santana Afton, Commented Mar 26, 2019 at 16:41

Santana Afton · Accepted Answer · 2019-03-26 04:22:15Z

1

Here’s a hint.

Assume that $(1,2)$ was part of this relation you want. Since the relation is symmetric, ...

we must have $(2,1)$ in our relation.

Furthermore, since the relation is transitive, that means ...

$(1,2)$ and $(2,1)$, along with transitivity, imply that $(1,1)$ is also in our relation.

Now, what can be said about reflexivity?

answered Mar 26, 2019 at 4:22

Santana Afton

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