Read set regions

Each circle is a set: a group of things. The rectangle is the universe, meaning everything considered in this question. Space outside both circles still belongs to that universe.

Hatching marks a selected region. It does not mean that the region is empty, and the diagram does not tell you how many things are there.

A and B selects only their overlap. A or B selects everything in either circle, including the overlap. Here, or includes both.

A but not B selects the part of A outside B. Read each expression as a rule for which regions to include.

Not A selects everything in the rectangle that is outside A. That includes B's non-overlapping part and the area outside both circles.

It excludes all of A, including the part where A overlaps B. Selecting only B would be wrong: B includes some of A and misses the area outside both circles.

In longer expressions, work through the parentheses first. For example, A but not B is not the same as B but not A.

Look at the hatching: all of A and all of B are selected, including their overlap. The area outside both circles is not selected. Which expression matches?

This checkpoint gives a diagram and asks for its expression. In the practice, you read an expression and choose one of four diagrams.

Level 1 uses two sets. Levels 2 and 3 use three; level 3 adds more nested expressions. Every round has six questions.