Question

If $A=\{2,3,5\}$ and $B=\{5,7\}$, find the set with highest number of elements:

• A. $A\times B$
• B. $B\times A$
• C. $A\times A$
• D. $B\times B$

Answer 1

The correct option is C $A\times A$

$A=\{2,3,5\}$

$B=\{5,7\}$

$A\times B=\left\{\right(2,5),(2,7),(3,5),(3,7),(5,5),(5,7\left)\right\}$

$B\times A=\left\{\right(5,2),(5,3),(5,5),(7,2),(7,3),(7,5\left)\right\}$

$A\times A=\left\{\right(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5\left)\right\}$

$B\times B=\left\{\right(5,5),(5,7),(7,5),(7,7\left)\right\}$

$\therefore A\times A$ has the highest number of elements