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)
The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by
Let $A = \{1, 2, 3\}$. The total number of distinct relations that can be defined over $A$ is
Let $A=\{1,2\}$ and $B=\{3,4\} .$ Find the number of relations from $A$ to $B .$
Let $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$
Depict this relation using an arrow diagram.
The Fig shows a relation between the sets $P$ and $Q$. Write this relation
in roster form
What is its domain and range ?