Set Language & Venn Diagram
In this topic, you will learn about set language and how to represent sets using Venn diagrams. A set is a collection of well-defined objects, which are called elements. You will also become familiar with key terms such as universal set, subset, union, intersection, and complement.
Venn diagrams are visual tools that help you organise and analyse the relationships between different sets. You will learn how to use circles to represent sets, identify common or unique elements, and solve problems involving one or more sets.
Related Lessons:
Set Language Symbols
Here are some of the commonly tested Set Language symbols:
- \(\cap\) for intersection
- \(\cup\) for union
- \(\subset\) is a proper subset of
- \(\subseteq\) is a subset of
- An element of \(\in\) / Not an element of \(\notin\)
- \(\xi\) is universal set
- A’ is the complement of A
- \(n\left(A\right)\) is number of elements in set A
- The notation for null set is \(\emptyset\) or { }
Venn Diagram
A Venn diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by intersections of the circles.
The video above shows all the commonly tested Venn Diagram combinations.
Example 1
Shade the region representing the subset (𝐴∪𝐵)′.
Example 2
On the Venn Diagram below, shade the set 𝐴′∩𝐵′.
Example 3
Draw a labelled Venn diagram on the space provided to illustrate the following sets.
Show the position of each element clearly.
𝜉={𝑥: 𝑥 is a positive integer, 1<𝑥<16}
A={multiple of 3}
B={prime numbers}
Example 4
𝜉={𝑥:𝑥 is an integer such that 0≤𝑥≤10}
A={𝑥:𝑥 is a prime number}
B={𝑥:𝑥 is a perfect square}
C={𝑥:𝑥 is a factor of 36}
- Find n(B’)
- List the element(s) of the set (𝐴∩𝐶)
- Which of the following is not a subset of (𝐵∩𝐶)?
{ },{1}, {1, 4, 9}, {0, 9}