Let $U = \{1, 2, 3, 4, 5\}$, $A = \{1, 2, 3\}$ and $B = \{1, 2\}$. Represent the relationship between $U$, $A$ and $B$ using Venn diagrams.

Question

Accepted Answer

> [!TLDR]
> Since $B\subseteq A$ here, circle $B$ is drawn entirely inside circle $A$ (nested circles) within the rectangle for $U$.

> [!FORMULA]
> Venn diagram: if $B\subseteq A$, the circle for $B$ is drawn wholly inside the circle for $A$ (concentric/nested); both sit inside the rectangle for $U$.

1. Here $U=\{1,2,3,4,5\}$, $A=\{1,2,3\}$, $B=\{1,2\}$.
2. Check subset: is every element of $B$ in $A$? $1\in A$ ✓, $2\in A$ ✓. So $B\subseteq A$, meaning circle $B$ must be drawn fully inside circle $A$.
3. Draw a rectangle labelled $U$.
4. Inside it, draw a large circle labelled $A$ containing $1,2,3$.
5. Inside circle $A$, draw a smaller circle labelled $B$, nested within $A$, containing $1,2$ (leaving $3$ inside $A$ but outside $B$). …

Region	Description	Set notation
Inside $A$ only	Elements in $A$ but not in $B$	$A \setminus B$
Inside $B$ only	Elements in $B$ but not in $A$	$B \setminus A$
Overlap	Elements in both $A$ and $B$	$A \cap B$
Outside both	Elements in neither $A$ nor $B$	$(A \cup B)^c$

Q.Let $U = \{1, 2, 3, 4, 5\}$ , $A = \{1, 2, 3\}$ and $B = \{1, 2\}$ . Represent the relationship between $U$ , $A$ and $B$ using Venn diagrams.

Concept understanding — Venn Diagrams

Venn Diagrams: Seeing Sets as Pictures

The Intuition

The Precise Statement

Why They Work

A Simple Example

Q.Let U={1,2,3,4,5}U = \{1, 2, 3, 4, 5\}U={1,2,3,4,5}, A={1,2,3}A = \{1, 2, 3\}A={1,2,3} and B={1,2}B = \{1, 2\}B={1,2}. Represent the relationship between UUU, AAA and BBB using Venn diagrams.

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Q.Let $U = \{1, 2, 3, 4, 5\}$ , $A = \{1, 2, 3\}$ and $B = \{1, 2\}$ . Represent the relationship between $U$ , $A$ and $B$ using Venn diagrams.

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