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If $A$ and $B$ be two sets such that $A \times B$ con sists of 6 elements. If three elements $\mathrm{A} \times \mathrm{B}$ are $(1,4),(2,6)$ and $(3,6)$, find $\mathrm{B} \times \mathrm{A}$.
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Verified Answer
The correct answer is:
$\{(4,1),(4,2),(4,3),(6,1),(6,2),(6,3)\}$
Since, $(1,4),(2,6)$ and $(3,6)$ are the elements of $\mathrm{A} \times \mathrm{B}$, therefore $1,2,3$ are the elements of $A$ and 4,6 are the elements of $B$.
Also, $\mathrm{A} \times \mathrm{B}$ has 6 elements
$\therefore \quad A=\{1,2,3\}$
and $B=\{4,6\}$
$\therefore B \times A=\{(4,1),(4,2),(4,3),(6,1),(6,2)$
$(6,3)\}$
and $B=\{4,6\}$
$\therefore \mathrm{B} \times \mathrm{A}=\{(4,1),(4,2),(4,3),(6,1),(6,2),$,
$(6,3)\}$
Also, $\mathrm{A} \times \mathrm{B}$ has 6 elements
$\therefore \quad A=\{1,2,3\}$
and $B=\{4,6\}$
$\therefore B \times A=\{(4,1),(4,2),(4,3),(6,1),(6,2)$
$(6,3)\}$
and $B=\{4,6\}$
$\therefore \mathrm{B} \times \mathrm{A}=\{(4,1),(4,2),(4,3),(6,1),(6,2),$,
$(6,3)\}$
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