First slide

Operations on Sets

Question

If $A = \{3^{n} : n \in N, n \leq 6\}, B = \{9^{n} : n \in N, n \leq 4\}$ then which of the following is false

Moderate

A

$\begin{aligned} A Δ B = {3, 27, 243, 6561} \end{aligned}$
B

$A ~ B = {3, 27, 243}$
C

$\begin{aligned} A \cap B = {9, 81, 729} \end{aligned}$
D

$A \cup B = {3, 9, 27, 81, 243, 729, 6561}$

Solution

$\begin{array}{l} A = {3, 9, 27, 81, 243, 729}, B = {9, 81, 729, 6561} \\ A \cup B = {3, 9, 27, 81, 243, 729, 6561} \\ A \cap B = {9, 81, 729} \\ A ~ B = {3, 27, 243} \\ B ~ A = {6561} \\ A Δ B = (A ~ B) \cup (B ~ A) = {3, 27, 243, 6561} \end{array}$

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