Question

Match the following for sets:$A=\{12,14,15,16,19,20\}B=\{18,21,20,15,17,13\}C=\{21,23,12,16,14,18\}$

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

Answer 1

Here we have three sets, $A=\{12,14,15,16,19,20\}$
$B=\{18,21,20,15,17,13\}$
$C=\{21,23,12,16,14,18\}$

Now, we have to find $A-B,B-A,A-C\&B-C$
We know difference of any two sets $X\&Y$ is the set of all elements of $X$ which are not in $Y.$
Or,
$X-Y=X-(X\cap Y)$
Using this let's find all the difference of sets.
$1.A-B=A-(A\cap B)$
$\Rightarrow A-B=\{12,14,15,16,19,20\}-\{15,20\}$
$\Rightarrow A-B=\{12,14,16,19\}$

$2.B-A=B-(A\cap B)$
$\Rightarrow A-B=\{18,21,20,15,17,13\}-\{15,20\}$
$\Rightarrow A-B=\{18,21,17,13\}$

$3.A-C=A-(A\cap C)$
$\Rightarrow A-C=\{12,14,15,16,19,20\}-\{12,14,16\}$
$\Rightarrow A-C=\{15,19,20\}$

$4.B-C=B-(A\cap C)$
$\Rightarrow A-B=\{18,21,20,15,17,13\}-\{18,21,20\}$
$\Rightarrow A-B=\{15,17,13,20\}$