What is a geometric relation?

Question

We will call a relation geometric if $∀x, y, z(xRy ∧ xRz → yRz)$

Prove that if a relation is geometric and reflexive, then it is also symmetric.

I'm trying to solve this problem but I don't understand the question. I've heard of Reflexive, Symmetric, Transitive, and equivalence relation, but not geometric?

But you have the definition there... – amrsa Nov 14 '20 at 17:10 — amrsa, Nov 14 '20 at 17:10

score 1 · Answer 1 · answered Nov 14 '20 at 17:13

1

You want to prove that $xRy$ implies $yRx$.
So suppose that $xRy$; since $R$ is reflexive, you have that $xRx$.
So, just take $z=x$ in the definition and obtain $yRx$.

answered Nov 14 '20 at 17:13

amrsa

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What is a geometric relation?

1 Answers1