Set notation

Description

A set is a collection of elements. Venn diagrams use overlapping circles inside a rectangle (the universal set $\xi$) to show how sets relate.

Key notation:

• $A \cup B$ — union: elements in $A$ or $B$ (or both)
• $A \cap B$ — intersection: elements in both $A$ and $B$
• $A'$ — complement: elements not in $A$
• $\emptyset$ — the empty set (no elements)
• $n(A)$ — the number of elements in set $A$

Example: If $\xi = {1,2,3,4,5,6,7,8}$, $A = {2,4,6,8}$ and $B = {1,2,3,4}$, then: $$A \cap B = {2, 4}, \quad A \cup B = {1,2,3,4,6,8}$$

Venn diagrams are also used in probability — write frequencies or probabilities in each region and make sure they sum correctly.

Common error: placing elements that belong to both sets in only one circle, not in the intersection. Also confusing union ($\cup$) with intersection ($\cap$) — remember $\cup$ looks like a U for "union".

Links

Probability sum Theoretical probabilities