Question

If $A=\{1,2,3\}$ and $B=\{4,5\},$ then $A\times B=$ ___.

• A. $\left\{\right(1,2),(1,3),(2,3),(4,5\left)\right\}$
• B. $\left\{\right(4,1),(4,2),(4,3),(5,1),(5,2),(5,3\left)\right\}$
• C. $\left\{\right(1,4),(1,5),(2,4),(2,5),(3,4),(3,5\left)\right\}$
• D. $\left\{\right(1,4),(1,5),(2,4),(2,5\left)\right\}$

Answer 1

The correct option is C

$\left\{\right(1,4),(1,5),(2,4),(2,5),(3,4),(3,5\left)\right\}$

The Cartesian product of sets A and B is defined as:
$A\times B=\left\{\right(a,b):a\in A,b\in B\}$
$\Rightarrow A\times B=\left\{\right(1,4),(1,5),(2,4),(2,5),(3,4),(3,5\left)\right\}$