If $A=\{2,3,4,5,6,7,8,9\}$ and let $R$ be the relation on $A$ defined by $\{(x, y): x, y \in A, x$ is a multiple of $y$ and $x \neq y\}$, then relation R is given as. _________________
Answer
$R=\{(4,2)(6,2)(8,2)(6,3)(9,3)(8,4)\}$, because relation is defined as $R =\{(x, y): x, y \in A, x$ is a multiple of $y$ and $x \neq y\}$ on the set $A=\{2,3,4,5,6$, $7,8,9\}$.
If $R=\{(x, y): x, y \in N, x+2 y=21\}$, then range of $R =$ _________________
Answer
$\{1,2,3, \ldots, 10\}$, because Given, $x+2 y=21 \Rightarrow x=21-2 y$ When $y=1, x=21-2 \times 1=19$ When $y=2, x=21-2 \times 2=17$ When $y=3, x=21-2 \times 3=15$ ... ... ... ... ... ... When $y=10, x=21-2 \times 10=1$ For other values of $y \in N$, we do not get $x \in N$. Range of $R=\{1,2,3, \ldots, 10\}$
If $A=\{1,5\}, B=\{2,6\}$ and $C=\{2,4\}$, then $A \times(B \cap C)=$ _________________.
Answer
$\{(1,2),(5,2)\}$, because it is given that, $A=\{1,5\}, B$ $=\{2,6\}$ and $C=\{2,4\}$ Then, $B \times C=\{2\}$ and $A \times$ $(B \cap C)=\{1,5\} \times\{2\}=\{(1,2),(5,2)\}$