Exam (9$\ ^{th\ }$ April 1 $1^{st\ }$ Shift 2024) 9th April Shift 1
Mathematics
Let A={2,3,6,7} and B={4,5,6,8}. Let R be a
relation defined on A×B by (a1,b1)R(a2,b2) if and only
if a1+a2=b1+b2. Then the number of elements in
R is .
Explanation
(25) : Given, A={2,3,0,7} and B={4,5,6,8}
\begin{longtable}[]{@{}
>{\raggedright\arraybackslash}p{(\columnwidth - 2\tabcolsep) * \real{0.4521}}
>{\raggedright\arraybackslash}p{(\columnwidth - 2\tabcolsep) * \real{0.5479}}@{}}
\toprule()
\begin{minipage}[b]{\linewidth}\raggedright
(a1,b1)R(a2,b2)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
⇒a1+a2=b1+b2
\end{minipage} \\
\begin{minipage}[b]{\linewidth}\raggedright
(2,4)R(6,4)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
(3,6)R(7,4)
\end{minipage} \\
\begin{minipage}[b]{\linewidth}\raggedright
(2,4)R(7,5)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
(3,5)R(7,5)
\end{minipage} \\
\begin{minipage}[b]{\linewidth}\raggedright
(2,5)R(7,4)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
(6,5)R(7,8)
\end{minipage} \\
\begin{minipage}[b]{\linewidth}\raggedright
(3,4)R(6,5)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
(6,8)R(7,5)
\end{minipage} \\
\begin{minipage}[b]{\linewidth}\raggedright
(3,5)R(6,4)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
(7,6)R(7,8)
\end{minipage} \\
\begin{minipage}[b]{\linewidth}\raggedright
(3,4)R(7,6)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
(6,4)R(6,8)
\end{minipage} \\
\begin{minipage}[b]{\linewidth}\raggedright
(6,6)R(6,6)
\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright
\end{minipage} \\
\midrule()
\endhead
\bottomrule()
\end{longtable}
Hence, total number of elements =13×2−1=25
\begin{enumerate}
\def\labelenumi{\arabic{enumi}.}
\setcounter{enumi}{40}
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