Venn diagrams are used to describe the relationship of the sets. The description of some sets is given and you are asked to draw a Venn diagram to illustrate the sets. You are well known about the triangles that they are having three sides. Based on their sides and the angles, it is classified into different types. The relationship of the triangles can also be described using Venn diagrams.
Venn diagrams:
Venn diagrams to determine the relationships between the sets such as subsets and intersections.
Venn diagram for A within B :
Here, all members of A belongs to B or A ⊂ B or A ∪ B = B or A ∩ B = A or n(A ∩ B) = n(A).
Venn diagram for A overlap B:
Here, some members of A belongs to B or A ∩ B ≠ Ø or n(A ∩ B ) ≠ 0
Venn diagram for disjoint sets of A and B :
Here, no members of A belongs to B or A ∩ B = Ø or n(A ∩ B ) = 0
Triangles:
scalene triangle:
A triangle is said to be scalene triangle, if all the sides are of different lengths.Some scalene triangles are also right triangles.
Right triangle:
A triangle is said to be right triangle, if one interior angle is exactly 90°. Some right triangles are also scalene triangles.
Equilateral triangle:
A triangle is said to be equilateral triangle, if all the sides are of same length.
Isosceles triangle:
A triangle is said to be isosceles triangle, if two sides are of same length and two angles are equal.
Examples
Let U is the set of triangles, A is the set of isosceles triangles, B is the set of equilateral triangles and C is the set of right-angled triangles.
Draw a Venn diagram.
Solution:
We have to determine the relationships between the sets.
All the equilateral triangles are said to be isosceles triangles, so B ⊂ A. (within)
Some of the right-angled triangles are said to be isosceles triangle. C ∩ A ≠ Ø (overlap)
No right-angled triangles are equilateral triangles. C ∩ B = Ø (disjoint)
Venn diagram for the triangles:
Let U is the set of triangles, S is the set of scalene triangles and R is the set of right triangles.
Draw the Venn diagram
Solution:
The relationship between scalene and right triangle to be defined.
Some of the right triangles are scalene triangles.
Triangles and Venn Diagrams
Venn diagrams:
Venn diagrams to determine the relationships between the sets such as subsets and intersections.
Venn diagram for A within B :
Here, all members of A belongs to B or A ⊂ B or A ∪ B = B or A ∩ B = A or n(A ∩ B) = n(A).
Venn diagram for A overlap B:
Here, some members of A belongs to B or A ∩ B ≠ Ø or n(A ∩ B ) ≠ 0
Venn diagram for disjoint sets of A and B :
Here, no members of A belongs to B or A ∩ B = Ø or n(A ∩ B ) = 0
Triangles:
scalene triangle:
A triangle is said to be scalene triangle, if all the sides are of different lengths.Some scalene triangles are also right triangles.
Right triangle:
A triangle is said to be right triangle, if one interior angle is exactly 90°. Some right triangles are also scalene triangles.
Equilateral triangle:
A triangle is said to be equilateral triangle, if all the sides are of same length.
Isosceles triangle:
A triangle is said to be isosceles triangle, if two sides are of same length and two angles are equal.
Examples
Let U is the set of triangles, A is the set of isosceles triangles, B is the set of equilateral triangles and C is the set of right-angled triangles.
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Draw a Venn diagram.
Solution:
We have to determine the relationships between the sets.
All the equilateral triangles are said to be isosceles triangles, so B ⊂ A. (within)
Some of the right-angled triangles are said to be isosceles triangle. C ∩ A ≠ Ø (overlap)
No right-angled triangles are equilateral triangles. C ∩ B = Ø (disjoint)
Venn diagram for the triangles:
Let U is the set of triangles, S is the set of scalene triangles and R is the set of right triangles.
Draw the Venn diagram
Solution:
The relationship between scalene and right triangle to be defined.
Some of the right triangles are scalene triangles.
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