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?
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 $yRx$.