Question

Let A and B be two sets such that $A\times B=\{(a,1),(b,3),(a,3),(b,1),(a,2),(b,2)\},$ then

• A. $A=\{1,2,3\}$ and $B=\{a,b\}$
• B. $A=\{a,b\}$ and$B=\{1,2,3\}$
• C. $A=\{1,2,3\}$ and $B\subset \{a,b\}$
• D. $A\subset \{a,b\}$ and $B\subset \{1,2,3\}$

Answer 1

The correct option is B $A=\{a,b\}$ and$B=\{1,2,3\}$

$A$ is the first element in the cartesian product $A\times B=\{a,b,a,b,a,b\}$

and $B$ is the second element in the cartesian product $A\times B=\{1,3,3,1,2,2\}$

$\therefore$ elements of $A=\{a,b\}$ and $B=\{1,2,3\}$