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8.4: Venn Diagrams

Cognitive Psychology · LibreTexts

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    From LibreTexts, under CC BY 4.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    To visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18th century. These illustration show called Venn Diagrams.

    Definition: Venn Diagrams

    A Venn diagram represents each set by a circle, usually drawn inside of a containing box representing the universal set. Overlapping areas indicate elements common to both sets.

    Basic Venn diagrams can illustrate the interaction of two or three sets.

    Example 1

    Create Venn diagrams to illustrate A ⋃ B, A ⋂ B, and Ac ⋂ B A ⋃ B contains all elements in either set.

    1.png
    Figure 10. Circles A & B

    A ⋂ B contains only those elements in both sets – in the overlap of the circles.

    2.png
    Figure 11. Circles A & B

    Ac will contain all elements not in the set A. Ac ⋂ B will contain the elements in set B that are not in set A.

    3.png
    Figure 12. Circles A & B

    Example 2

    Use a Venn diagram to illustrate (H ⋂ F)c ⋂ W

    We’ll start by identifying everything in the set H ⋂ F

    4.png
    Figure 13. Circles H, F, & W

    Now, (H ⋂ F)c ⋂ W will contain everything not in the set identified above that is also in set W.

    5.png
    Figure 14. Circles H, F, & W

    Example 3

    Create an expression to represent the outlined part of the Venn diagram shown.

    The elements in the outlined set are in sets H and F, but are not in set W. So we could represent this set as H ⋂ F ⋂ Wc

    6.png
    Figure 15. Circles H, F, & W

    Try it Now

    Create an expression to represent the outlined portion of the Venn diagram shown

    7.png
    Figure 16. Circles A, B, & C

    This page titled 8.4: Venn Diagrams was last modified on Tue, 01 Sep 2026 19:09:19 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Mehgan Andrade and Neil Walker.