What is Intersection and union?

Example 1.8

Take $I = \intcc{-1}{3}$ and $J = \intoo{1}{5}$. Draw both on the same line: they overlap between $1$ and $3$. Therefore

Note the brackets: $1 \notin J$ so $1 \notin I \cap J$, but $3 \in I$ and $3 \in J$, so $3 \in I \cap J$.