Question

For A={5,10,15,20}; B={6,10,12,18,24} and C={7,10,12,14,21,28}, verify whether $A$\$(B$ \ $C)$$=(A$\ $B)$ \ $C$. Justify your answer

Answer 1

The given sets are $A=\{5,10,15,20\}$, $B=\{6,10,12,18,24\}$ and $C=\{7,10,12,14,21,28\}$

Let us first find $A\setminus (B\setminus C)$ as follows:

$A\setminus (B\setminus C)=\{5,10,15,20\}\setminus (\{6,10,12,18,24\}\setminus \{7,10,12,14,21,28\})=\{5,10,15,20\}\setminus \{6,18,24\}$
$=\{5,10,15,20\}........\left(1\right)$

Now we find $(A\setminus B)\setminus C$as follows:

$(A\setminus B)\setminus C=(\{5,10,15,20\}\setminus \{6,10,12,18,24\})\setminus \{7,10,12,14,21,28\}=\{5,15,20\}\setminus \{7,10,12,14,21,28\}$

$=\{5,15,20\}........\left(2\right)$

Since equation 1 is not equal to equation 2,

Hence, $A\setminus (B\setminus C)\ne (A\setminus B)\setminus C$