🔢 Set It Right! Mastering Unions & Intersections

In O-Level Mathematics, **set notation** is a foundational language that lets us describe and organise data quickly. Whether you are counting students who play football, basketball, or both, or analysing survey results, understanding sets,

n(A)

, union

\cup

, and intersection

\cap

will make many exam problems far simpler.

Main Concepts

$A, B$ are sets. $n(A)$ means **the number of elements** in set $A$ .
Union: $A \cup B$ contains all elements that are in $A$ **or** $B$ (or both).
Intersection: $A \cap B$ contains elements that are in **both** $A$ **and** $B$ .

Worked Example: Exam-Style Question

Problem: In a class of 30 students, 18 study Chemistry (

C

), 15 study Physics (

P

) and 9 study both subjects. Find (i)

n(C \cup P)

, (ii) the number who study neither subject. Step 1: Use the union formula

n(C \cup P) = n(C) + n(P) - n(C \cap P)

n(C \cup P) = 18 + 15 - 9 = 24.

Step 2: Students who study neither subject

= 30 - n(C \cup P) = 30 - 24 = 6.