Let $A = {3, 6, 9, 12, 15, 18, 21, 24}$ and $B = {4, 8, 12, 16, 20, 24}$ . Find both $A ∖ B$ and $B ∖ A$

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Solution

By definition, $A ∖ B$ is all those elements in $A$ which are not in $B$ . We can read them: $3, 6, 9, 15, 18, 21$ . Hence
$A ∖ B = {3, 6, 9, 15, 18, 21}$ .
Similarly,
$B ∖ A = {4, 8, 16, 20}$ .
What is $A \cup (B ∖ A)$ ? Observe
${3, 6, 9, 12, 15, 18, 21, 24} \cup {4, 8, 16, 20} = {3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 21, 24}$ .
This is precisely $A \cup B$ . Do you also observe $A \cap (B ∖ A) = / 0$ ?

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