Question

If $A=\{x:x=3^n,n\le 6,nϵN\}$ and $B=\{x:x=9^n,n\le 4,nϵN\}$, then which of the following is false?

• A. $A\cup B=\{3,9,27,81,243,729,6561\}$
• B. $A\cap B=\{9,81,729,6561\}$
• C. $A-B=\{3,27,243\}$
• D. $A\Delta B=\{3,27,243,6561\}$

Answer 1

The correct option is B $A\cap B=\{9,81,729,6561\}$

$A=\{3^1,3^2,3^3,3^4,3^5,3^6\}$
$=\{3,9,27,81,243,729\}$
and $B=\{9^1,9^2,9^3,9^4\}=\{9,81,729,6561\}$
(a) $A\cup B=\{3,9,27,81,243,729,6561\}$
(b) $A\cap B=\{9,81,729\}$
(c) $A-B=\{3,27,243\}$
(d) $A\Delta B=(A-B)\cup (B-A)$
$=\{3,27,243\}\cup \left\{6561\right\}=\{3,27,243,6561\}$
$\therefore$ Answer is (b).