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 $A=\{1,2,3,4,5,6\} .$ Define a relation $R$ from $A$ to $A$ by $R=\{(x, y): y=x+1\}$
Write down the domain, codomain and range of $R .$
The relation $R$ defined on the set of natural numbers as $\{(a, b) : a$ differs from $b$ by $3\}$, is given by
The Fig shows a relation between the sets $P$ and $Q$. Write this relation
in roster form
What is its domain and range ?
Given two finite sets $A$ and $B$ such that $n(A) = 2, n(B) = 3$. Then total number of relations from $A$ to $B$ is
Let $R$ be a relation from $N$ to $N$ defined by $R =\left\{(a, b): a, b \in N \text { and } a=b^{2}\right\} .$ Are the following true?
$(a, a) \in R ,$ for all $a \in N$