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If $A=\{1,2,5,6\}$ and $B=\{1,2,3\}$, then $(A \times B) \cap(B \times A)$ is equal to
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Verified Answer
The correct answer is:
$\{(1,1),(1,2),(2,1),(2,2)\}$
Given, $A=\{1,2,5,6\}$ and $B=\{1,2,3\}$
$$
\begin{aligned}
A \times B=\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),\\
&(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)\} \\
B \times A=&\{(1,1),(1,2),(1,5),(1,6),(2,1),(2,2),\\
&(2,5),(2,6),(3,1),(3,2),(3,5),(3,6)\} \\
\therefore(A \times B) \cap(B \times A)=\{(1,1),(1,2),(2,1),(2,2)\}
\end{aligned}
$$
$$
\begin{aligned}
A \times B=\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),\\
&(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)\} \\
B \times A=&\{(1,1),(1,2),(1,5),(1,6),(2,1),(2,2),\\
&(2,5),(2,6),(3,1),(3,2),(3,5),(3,6)\} \\
\therefore(A \times B) \cap(B \times A)=\{(1,1),(1,2),(2,1),(2,2)\}
\end{aligned}
$$
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