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

(N/A) We have,$V - B = \{e, o\}$,since the elements $e, o$ belong to $V$ but not to $B$.
$B - V = \{k\}$,since the element $k$ belongs to $B$ but not to $V$.
We note that $V - B \neq B - V$. Using the set-builder notation,we can rewrite the definition of difference as:
$A - B = \{x : x \in A \text{ and } x \notin B\}$.
The difference of two sets $A$ and $B$ can be represented by a Venn diagram as shown in the figure below.
The shaded portion represents the difference of the two sets $A$ and $B$.