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If $A=\{1,2,5,6\}$ and $B=\{1,2,3\}$, then what is $(A \times B) \cap(B \times A)$ equal to?
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Verified Answer
The correct answer is:
$\{(1,1),(1,2),(2,1),(2,2)\}$
LetA $=\{1,2,5,6\}$ and $\mathrm{B}=\{1,2,3\}$ $\mathrm{A} \times \mathrm{B}=\{(1,1),(1,2),(1,3),(2,1),(2,2),(2,3)$
$(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)\}$
and $\mathrm{B} \times \mathrm{A}=\{(1,1),(1,2),(1,5),(1,6),(2,1),(2,2)$,
$(2,5),(2,6),(3,1),(3,2),(3,5),(3,6)\}$
$\Rightarrow \quad(\mathrm{A} \times \mathrm{B}) \cap(\mathrm{B} \times \mathrm{A})$
$=\{(1,1),(1,2),(2,1),(2,2)\}$
$(5,1),(5,2),(5,3),(6,1),(6,2),(6,3)\}$
and $\mathrm{B} \times \mathrm{A}=\{(1,1),(1,2),(1,5),(1,6),(2,1),(2,2)$,
$(2,5),(2,6),(3,1),(3,2),(3,5),(3,6)\}$
$\Rightarrow \quad(\mathrm{A} \times \mathrm{B}) \cap(\mathrm{B} \times \mathrm{A})$
$=\{(1,1),(1,2),(2,1),(2,2)\}$
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