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 $B$
Similar Questions
In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement ?
In a school, there are three types of games to be played. Some of the students play two types of games, but none play all the three games. Which Venn diagrams can justify the above statement ?
- [JEE MAIN 2021]
If $X$ and $Y$ are two sets such that $X \cup Y$ has $18$ elements, $X$ has $8$ elements and $Y$ has $15$ elements ; how many elements does $X \cap Y$ have?
If $X$ and $Y$ are two sets such that $X \cup Y$ has $18$ elements, $X$ has $8$ elements and $Y$ has $15$ elements ; how many elements does $X \cap Y$ have?
If $A=\{1,2,3,4\}, B=\{3,4,5,6\}, C=\{5,6,7,8\}$ and $D=\{7,8,9,10\} ;$ find
$A \cup B \cup C$
If $A=\{1,2,3,4\}, B=\{3,4,5,6\}, C=\{5,6,7,8\}$ and $D=\{7,8,9,10\} ;$ find
$A \cup B \cup C$
If $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number $\} $ $C = \{ x:x$ is an odd natural number $\} $ and $D = \{ x:x$ is a prime number $\} ,$ find
$C \cap D$
If $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number $\} $ $C = \{ x:x$ is an odd natural number $\} $ and $D = \{ x:x$ is a prime number $\} ,$ find
$C \cap D$
If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {1 \over x},\,0 \ne x \in R\} $ $B = \{ (x,y):y = - x,x \in R\} $, then
If the sets $A$ and $B$ are defined as $A = \{ (x,\,y):y = {1 \over x},\,0 \ne x \in R\} $ $B = \{ (x,y):y = - x,x \in R\} $, then