Question

For two sets $A\&B$ such that:
$A=\{12,14,15,16,19,20\}$
$B=\{18,21,20,15,17,13\}$
Choose the correct options.

• A. $A△B=\{12,14,16,19,18,21,17,13\}$
• B. $A△B=\{15,16,20\}$
• C. $B△A=\{12,14,16,19,18,21,17,13\}$
• D. $B△A=\{15,16,20\}$

Answer 1

Answer: (A), (C)

$B△A=\{12,14,16,19,18,21,17,13\}$

Given two sets $A\&B$ such that:
$A=\{12,14,15,16,19,20\}$
$B=\{18,21,20,15,17,13\}$
$A△B=(A-B)\cup (B-A)$
Now, $A-B=\{12,14,16,19\}$ and $B-A=\{18,21,17,13\}$
$\Rightarrow A△B=(A-B)\cup (B-A)$
$=\{12,14,16,19\}\cup \{18,21,17,13\}$
$=\{12,14,16,19,18,21,17,13\}$

Now, we know the commutative property, i.e.,
$A△B=B△A=\{12,14,16,19,18,21,17,13\}$