🧩 Sets & Matrices
Sets and Matrices cover set notation, Venn diagrams, union/intersection, matrix operations, and inverse matrices. These topics are relatively newer additions to the E-Math syllabus and are very scorable with consistent practice. Many students find sets intuitive, and matrix questions follow predictable patterns.
Sets questions often appear as word problems involving surveys, club memberships, or student activities. The key tool is the Venn diagram, which provides a visual way to organise information about overlapping groups. Matrix questions typically test arithmetic operations and the ability to interpret matrices in real-world contexts (e.g., quantities and prices).
Set Notation & Terminology
A set is a well-defined collection of distinct objects called elements or members. We use curly brackets to list elements: A = {1, 2, 3, 4, 5}. The symbol \in means "is an element of" and \notin means "is not an element of". The universal set (denoted by a script E or U) contains all elements under consideration in a particular problem.
Understanding set notation precisely is crucial because exam questions often ask you to shade regions on Venn diagrams or describe sets using notation. A common exam task is to express a shaded region using union, intersection, and complement symbols.
Set Notation Essentials
Union (A ∪ B)
Elements in A OR B (or both). On a Venn diagram, this is everything inside either circle.
Intersection (A ∩ B)
Elements in BOTH A AND B simultaneously. The overlapping region in a Venn diagram.
Complement (A')
Elements NOT in A but still in the universal set. Everything outside circle A.
Subset (A ⊂ B)
Every element of A is also in B. Circle A is entirely inside circle B. Also written A ⊆ B.
Empty Set (∅)
A set with no elements. A ∩ B = ∅ means A and B have no overlap (mutually exclusive / disjoint).
n(A)
The number of elements in set A. For example, if A = {2, 4, 6}, then n(A) = 3.
Key Venn Diagram Formula
For two sets A and B: n(A \cup B) = n(A) + n(B) - n(A \cap B). We subtract the intersection because those elements are counted twice (once in A and once in B). This formula is the basis for solving almost all Venn diagram word problems.
📝Worked Example 1: Two-Set Venn Diagram
In a class of 40 students, 25 play football, 18 play basketball, and 8 play both. How many play (a) at least one sport? (b) neither sport? (c) football only?
Venn diagram showing union, intersection, and complement regions
📝Worked Example 2: Three-Set Venn Diagram
In a survey of 100 people: 60 like tea, 50 like coffee, 30 like juice, 20 like both tea and coffee, 15 like both tea and juice, 10 like both coffee and juice, 5 like all three. Find how many like none of them.
Three-set Venn diagram showing all intersection regions
📝Worked Example 3: Shading Venn Diagrams
Shade the region representing (A \cup B)' \cap C on a three-set Venn diagram.
Three-set Venn diagram showing all intersection regions
What the full chapter covers
Set Notation & Terminology
Matrix Operations
Inverse of a 2 x 2 Matrix
Matrices in Real-World Context
Set Builder Notation and Number Sets
Key Venn Diagram Formula
Matrix Multiplication Rule
De Morgan's Laws
Sets & Matrices Are Scoring Topics!
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