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 $R$ be a relation from $Q$ to $Q$ defined by $R=\{(a, b): a, b \in Q$ and $a-b \in Z \} .$ Show that
$(a, b) \in R$ and $(b, c) \in R$ implies that $(a, c) \in R$
Let $R$ be the relation on $Z$ defined by $R = \{ (a,b):a,b \in Z,a - b$ is an integer $\} $ Find the domain and range of $R .$
The Fig shows a relationship between the sets $P$ and $Q .$ Write this relation
in set-builder form
What is its domain and range?
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\} $
Write $R$ in roster form
Determine the domain and range of the relation $R$ defined by $R =\{(x, x+5): x \in\{0,1,2,3,4,5\}\}$