What does aIb here mean?

Question

"An incidence system consists of two sets $S$ and $T$ together with a relation $I$. If $aIb, a ∈ S, b ∈ T$, then we call $a$ and $b$ incident."

Answer 1

$I$ is a subset of $S \times T$ and $a I b$ means that $(a,b) \in I$. It's a standard convention.

For example: Let $<$ be the natural strict order of natural numbers. $<$ is a subset of $\mathbb N \times \mathbb N$ and we write $m < n$ iff $(m,n) \in <$ iff $m$ is smaller than $n$.