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