Let $X = \{ 1,\,2,\,3,\,4,\,5\} $ and $Y = \{ 1,\,3,\,5,\,7,\,9\} $. Which of the following is/are relations from $X$ to $Y$
${R_1} = \{ (x,\,y)|y = 2 + x,\,x \in X,\,y \in Y\} $
${R_2} = \{ (1,\,1),\,(2,\,1),\,(3,\,3),\,(4,\,3),\,(5,\,5)\} $
${R_3} = \{ (1,\,1),\,(1,\,3)(3,\,5),\,(3,\,7),\,(5,\,7)\} $
both (B) and (C)
Let $A=\{x, y, z\}$ and $B=\{1,2\} .$ Find the number of relations from $A$ to $B$.
Let $A=\{1,2,3,4,6\} .$ Let $R$ be the relation on $A$ defined by $\{ (a,b):a,b \in A,b$ is exactly divisible by $a\} $
Find the domain of $R$
Let $A=\{1,2,3,4\}, B=\{1,5,9,11,15,16\}$ and $f=\{(1,5),(2,9),(3,1),(4,5),(2,11)\}$
Are the following true?
$f$ is a relation from $A$ to $B$
Justify your answer in each case.
The Fig shows a relationship between the sets $P$ and $Q .$ Write this relation
in set-builder form
What is its domain and range?
The Fig shows a relation between the sets $P$ and $Q$. Write this relation
in roster form
What is its domain and range ?