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

Question

Accepted Answer

> [!TLDR]
> Since $A$ and $B$ share no common element, they are drawn as two disjoint (non-overlapping) circles inside the rectangle for $U$.

> [!FORMULA]
> Venn diagram: $U$ = rectangle; if $A\cap B=\phi$, circles for $A$ and $B$ are drawn **not overlapping**; elements of $U$ in neither $A$ nor $B$ sit outside both circles but inside the rectangle.

1. Here $U=\{1,2,3,4,5\}$, $A=\{1,2\}$, $B=\{3,5\}$.
2. Check $A\cap B$: common elements of $\{1,2\}$ and $\{3,5\}$ — none. So $A\cap B=\phi$, meaning the circles must NOT overlap.
3. Draw a rectangle labelled $U$.
4. Inside it, draw two separate non-touching circles, one labelled $A$ containing $1,2$, and another labelled $B$ containing $3,5$. …

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

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

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