Question

Let $V=\{a,e,i,o,u\}$ and $B=\{a,i,k,u\}$.
Find $V-B$ and $B-V$.

Answer 1

Given: $V=\{a,e,i,o,u\}$ and $B=\{a,i,k,u\}$
Step 1: Finding $V-B$
By definition difference of sets $V$ and $B$ in this order i.e. $V-B$ is the set of elements which belong to $V$ but not to $B$.
Now, $V-B=\{a,e,i,o,u\}-\{a,i,k,u\}$={$e,o$}
$\because$ Elements $e,o$ belong to $V$ but not to $B$

Step 2: Finding $B-V$
$B-V=\{a,i,k,u\}-\{a,e,i,o,u\}=\left\{k\right\}$
$\because$ Elements $k$ belong to $B$ but not to $V$.

Alternatie Solution (By Venn-Diagram)
Given: $V=\{a,e,i,o,u\}$ and $B=\{a,i,k,u\}$
Step 1: Finding $V-B$
$\because V-B=V-(V\cap B)$
Here, $V\cap B=\{a,e,i,o,u\}\cap \{a,i,k,u\}=\{a,i,u\}$
Now, $V-B=\{a,e,i,o,u\}-\{a,i,u\}=\{e,o\}$
Step 2: Finding $B-V$

$\because B-V=B-(B\cap V)=B-(V\cap B)=\{a,i,k,u\}-\{a,i,u\}$
$\therefore B-V=\left\{k\right\}$