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Mathematics-Online course: Preparatory Course Mathematics - Basics - Sets

Operations on Sets

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The following operations can be applied to sets $ A$ and $ B$:

The so-called Venn-diagrams illustrate the set operations.

\includegraphics[width=.3\moimagesize]{venndiagramm_A} \includegraphics[width=.3\moimagesize]{venndiagramm_B} \includegraphics[width=.3\moimagesize]{venndiagramm_AuB}
$ A$ $ B$ union: $ A\cup B$
\includegraphics[width=.3\moimagesize]{venndiagramm_AnB} \includegraphics[width=.3\moimagesize]{venndiagramm_AoB} \includegraphics[width=.3\moimagesize]{venndiagramm_AdB}
intersection: $ A \cap B$ difference: $ A\setminus B$ symmetric difference: $ A\Delta B$

If $ B \subset A$, some of the above diagrams are identical to one another:

\includegraphics[width=.3\moimagesize]{venndiagramm_A2} \includegraphics[width=.3\moimagesize]{venndiagramm_B2} \includegraphics[width=.3\moimagesize]{venndiagramm_AoB2}
union: $ A = A\cup B$ intersection: $ B = A \cap B$ complement set : $ A \setminus B = A \Delta B$
(Authors: Höllig/Hörner/Knesch/Abele)

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  automatically generated 1/9/2017