Question

Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that $A\cup B$ can have.

Answer 1

If $A\subset B$ then $A\cup B$ = {$x:xϵB$}

$n(A\cup B)=7$

If $A\cap B\ne$ { }

then $n(A\cup B)<11$

If $A\cap B$ = { }

then $n(A\cup B)$= 11

The maximun number of elements that $A\cup B$ can have is 11.