Linear diagrams are a way of representing sets and their intersections.
  Where two sets share the same vertical space, it means they share members.

  For example, the diagram below represents the interests of a group of people.
  There are people who like football, but nothing else. We know that because there is some vertical space where
  the line labelled Football exists, but no other lines.

  Similarly, there are people who like football and golf, but not hockey or swimming.

  Some lines are drawn in several pieces. For example, the line labelled Golf is drawn in two pieces.
  There is nothing special about this. We are looking for overlapping vertical space with any piece of a line.
  For example, there are people who like golf and swimming, but nothing else.
  And, there are people who like football, golf and hockey but not swimming.