Question

Given $A=\{5,6,7\}$ and $B=\{6,8,10\}$, then : $(A\cup B)\times B$

Find the number of elements in the above set obtained.

Answer 1

$A=\{5,6,7\}$ and $B=\{6,8,10\}$
$\therefore A\cup B=\{5,6,7,8,10\}$
$(A\cup B)\times B=\{5,6,7,8,10\}\times \{6,8,10\}$
$=\{(5,6),(5,8),(5,10),(6,6),(6,8),(6,10),(7,6),(7,8),(7,10),(8,6),(8,8),(8,10),(10,6),(10,8),(10,10)\}$

Thus there are total $15$ elements obtained in the above set.