Exercises: Venn Diagrams

1, 3, 5 — the numbers written outside the circle but still inside the rectangle.

2, 4, 6 — the numbers written inside the circle labeled A.

1, 2, 3, 4, 5, 6 — every number shown anywhere in the diagram, inside or outside the circle.

A' — the complement of A, containing all elements of U that are not in A.

A ∩ A — the intersection of set A with itself, which would just give back set A again.

A second, entirely separate universal set that exists independently of U.

The two circles should overlap slightly, to show that some numbers might be shared.

The two circles should be drawn separately, not touching, since A and B share no elements at all.

Only one circle should be drawn, containing both A and B together.

The two circles should be drawn separately, not touching, since A and B are different sets.

Only one circle should be drawn, containing all of A and B combined.

The two circles should overlap, with 2 and 4 placed in the overlapping region shared by both circles.

{1, 2} — the elements found only in circle A and nowhere in circle B.

{3, 4} — the elements found in the overlapping region shared by both circles.

{1, 2, 3, 4, 5, 6} — every element found in either circle, combining both A and B entirely.

{3, 4} — only the elements shared by both circles, ignoring everything else in A and B.

{7, 8, 9, 10} — the elements sitting outside both circles but still inside the rectangle.

{1, 2, 3, 4, 5, 6} — every element found in circle A or circle B (or both).