Question

If $A=\{3,6,9,12,15,18,21\},B=\{4,8,12,16,20\}$, $C=\{2,4,6,8,10,12,14,16\},D=\{5,10,15,20\}$, find
$\left(i\right)A-B$
$\left(ii\right)A-C$
$\left(iii\right)A-D$
$\left(iv\right)B-A$
$\left(v\right)C-A$
$\left(vi\right)D-A$
$\left(vii\right)B-C$
$\left(vii\right)B-D$
$\left(ix\right)C-B$
$\left(x\right)D-B$
$\left(xi\right)C-D$
​​​​​​$\left(xii\right)D-C$

Answer 1

Given: $A=\{3,6,9,12,15,18,21\},B=\{4,8,12,16,20\}$, $C=\{2,4,6,8,10,12,14,16\},D=\{5,10,15,20\}$

$\therefore A-B=\{3,6,9,12,15,18,21\}-\{4,8,12,16,20\}=\{316,9,15,18,21\}$
Hence, $A-B=\{3,6,9,12,15,18,21\}$

$\therefore A-C=\{3,6,9,12,15,18,21\}-\{2,4,6,8,10,12,14,16\}=\{3,9,15,18,21\}$
Hence, $A-C=\{3,9,15,18,21\}$

$\therefore A-D=\{3,6,9,12,15,18,21\}-\{5,10,15,20\}=\{3,6,9,12,18,21\}$
Hence, $A-D=\{3,6,9,12,18,21\}$

$\therefore B-A=\{4,8,12,16,20\}-\{3,6,9,12,15,18,21\}=\{4,8,16,20\}$
Here, $B-A=\{4,8,16,20\}$

$\therefore C-A=\{2,4,6,8,10,12,14,16\}-\{3,6,9,12,15,18,21\}=\{2,4,8,10,14,16\}$
Hence, $C-A=\{2,4,8,10,14,16\}$

$\therefore D-A=\{5,10,15,20\}-\{3,6,9,12,15,18,21\}=\{5,10,20\}$
Hence, $D-A=\{5,10,20\}$

$\therefore B-C=\{4,8,12,16,20\}-\{2,4,6,8,10,12,14,16\}=\left\{20\right\}$
Hnce, $B-C=\left\{20\right\}$

$\therefore B-D=\{4,8,12,16,20\}-\{5,10,15,20\}=\{4,8,12,20\}$
Hence, $B-D=\{4,8,12,16\}$

$\therefore C-B=\{2,4,6,8,10,12,14,16\}-\{4,8,12,16,20\}=\{2,6,10,14\}$
Hence, $C-B=\{2,6,10,14\}$

$\therefore D-B=\{5,10,15,20\}-\{4,8,12,16,20\}=\{5,10,15\}$
Hence, $D-B=\{5,10,15\}$

$\therefore C-D=\{2,4,6,8,10,12,14,16\}-\{5,10,15,20\}=\{2,4,6,8,12,14,16\}$
Hence, $C-D=\{2,4,6,8,12,14,16\}$

$\therefore D-C=\{5,10,15,20\}-\{2,4,6,8,10,12,14,16\}=\{5,15,20\}$
Hence, $D-C=\{5,15,20\}$