Types of Venn diagrams and how they are used
There are three types of Venn diagram situations when two sets are involved.
The two sets are different. One set is a subset of the other.
There is an intersection.
Here are some examples of each type, with some of the language that could be used.
Discrete sets
Odd numbers and even numbers. “No odd numbers are even numbers.”
Others: Quadrilaterals and triangles. Positive numbers and negative numbers.
Set and subset
The set of multiples of 6 is a subset of the set of multiples of 3.
“All multiples of 6 are multiples of 3. Some multiples of 3 are multiples of 6.”
Set of multiples of 6 is {6, 12, 18, 24 …} Set of multiples of 3 is {3, 6, 9, 12, 15 …}
Other examples
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The set of factors of 6 is a subset of the set of factors of 12. The smaller set is the set of
common factors.
The set of squares is a subset of the set of rectangles ... and similarly: parallelograms,
trapezia; rectangles, parallelograms; rhombuses, kites.
The set of shapes with two lines of symmetry is a subset of the set of shapes with one line of
symmetry.
The set of congruent shapes is a subset of the set of similar shapes, because congruent
shapes have a scale factor of 1.
Intersecting sets
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The set of multiples of 2 intersects the set of multiples of 3; the intersection is the set of
multiples of 6. The intersection is the set of common multiples. “Some multiples of 2 are
multiples of 3. Some multiples of 3 are multiples of 2.The intersection is the set of numbers
which are both multiples of 2 and multiples of 3.”
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The set of factors of 15 intersects with the set of factors of 12; the intersection is the set of
common factors of 15 and 12.
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The sets of square and cube numbers intersect. The intersection set includes 1 and 64.
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The set of rhombuses intersects the set of rectangles; the intersection is the set of squares.
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The set of shapes with mirror symmetry (letters: A, H, I, M etc.) intersects the set of shapes
with half turn symmetry (letters: H, I, N, S etc.) the intersection is the set of shapes with at
least two perpendicular lines of symmetry (letters: H, I, etc.).
Two-way tables
Each of the above can be represented by a two-way table. However we can also use a two-way grid
for situations with more than two values of at least one variable. For example: sex and age,
outcomes for two dice (each has 6 possible outcomes, so 36 possible outcomes for 2 dice), etc.
With Venn diagrams there are only two values - in the set or out of the set.