If $A=\left\{x: x=3^n, n \leq 6\right\}$ and $\left.B=\left(x: x=9^n, n \leq 4\right), n \in N\right\}$ then which of the following is false?
Answer & explanation
Correct answer: option 2
The correct answer is Option 2: $A \cap B=\{9,81,729,6561\}$
$A=\left\{3^1, 3^2, 3^3, 3^4, 3^5, 3^6\right\} =\{3,9,27,81,243,729\}$
and $B=\left\{9^1, 9^2, 9^3, 9^4\right\}=\{9,81,729,6561\}$
(a) $A \cup B=\{3,9,27,81,243,729,6561\}$
(b) $A \cap B=\{9,81,729\}$ and not $A \cap B=\{9,81,729,6561\}$ as mentioned.
(c) $A-B=\{3,27,243\}$
(d) $A \Delta B=(A-B) \cup(B-A)$
$=\{3,27,243\} \cup\{6561\}=\{3,27,243,6561\}$
Hence (2) is the correct answer.