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2.Relations and Functions
easy
Let $A$ and $B$ be two sets such that $n(A)=3$ and $n(B)=2 .$ If $(x, 1),(y, 2),(z, 1)$ are in $A \times B$, find $A$ and $B$, where $x, y$ and $z$ are distinct elements.
A
$\{ x,y,z\} $ and $\{ 1,2\} $
B
$\{ x,y,z\} $ and $\{ 1,2\} $
C
$\{ x,y,z\} $ and $\{ 1,2\} $
D
$\{ x,y,z\} $ and $\{ 1,2\} $
Solution
It is given that $n(A)=3$ and $n(B)=2 ;$ and $(x, 1),(y, 2),(z, 1)$ are in $A \times B$
We know that
$A=$ Set of first elements of the ordered pair elements of $A \times B$
$B =$ Set of second elements of the ordered pair elements of $A \times B$
$\therefore x, y,$ and $z$ are the elements of $A ;$ and $1$ and $2$ are the elements of $B$
Since $n(A)=3$ and $n(B)=2$
It is clear that $A=\{x, y, z\}$ and $B=\{1,2\}$
Standard 11
Mathematics
