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Venn Diagram Sets

Quiz A

Shade the Region

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Score

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Shade: —

Select the correct regions above, then check.

Quiz B

Identify the Set

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Which set is shaded?

Choose one of the options above.

Parts of Two Sets

A complete guide to all 16 set notations from two sets A and B.

Every Venn diagram with two sets A and B is divided into 4 disjoint parts:

\(A_0\) or \((A-B)\) — only in A

\(B_0\) or \((B-A)\) — only in B

\(A \cap B\) — in both A and B

\((A \cup B)'\) — outside both

Combining these 4 parts in all possible ways gives us \(\binom{4}{0}+\binom{4}{1}+\binom{4}{2}+\binom{4}{3}+\binom{4}{4} = 1+4+6+4+1 = \mathbf{16}\) distinct set notations.

Parts used	Count	Set Notations
0 parts	1	\(\varnothing\)
1 part	4	\(A_0,\ B_0,\ A\cap B,\ \overline{A\cup B}\)
2 parts	6	\(A,\ B,\ A',\ B',\ A\triangle B,\ (A\triangle B)'\)
3 parts	4	\(A\cup B,\ (A-B)',\ (B-A)',\ (A\cap B)'\)
4 parts	1	\(U\)