Q.If $A = \{a, b, c, d, e\}$ and $B = \{b, d, f, g\}$, find $A - B$ and $B - A$. What do you observe about $(A - B) \cap (B - A)$?

[!TLDR] $A-B$ and $B-A$ keep only each set's private elements, and never overlap. [!ANSWER] $A-B=\{a,c,e\}$, …

$A = \{a,b,c,d,e\}$, $B = \{b,d,f,g\}$. $A - B$ keeps elements of $A$ absent from $B$: removing $b,d$ (which are in $B$) from $A$ leaves $\{a,c,e\}$. $B - A$ keeps elements of $B$ absent from $A$: removing $b,d$ (which are in $A$) from $B$ leaves $\{f,g\}$. Comparing $\{a,c,e\}$ and $\{f,g\}$, they share no elements at all, so $(A-B)\cap(B-A) = \varnothing$ — this is not a coincidence of this example but a general fact: $A-B$ only ever contains elements of $A$, while $ …

Compute each difference by removing the other set's elements, then check for comm …

A common mistake is assuming $A-B$ and $B-A$ are the same set, or computing their intersection incorrectly …