Question

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

• 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

Answer: (B)

$A=\{3^1,3^2,3^3,3^4,3^5,3^6\}$
$=\{3,9,27,81,243,729\}$
$B=\{9^1,9^2,9^3,9^4\}$
$=\{9,81,729,6561\}$
(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) $A\Delta B=(A-B)\cup (B-A)$
$=\{3,27,243\}\cup \{6561\}$
$=\{3,27,243,6561\}$