A class list $A$ has the pupils who play football removed, leaving set $B$ behind. The remainder $A-B$ equals:

1. The difference $A-B$ holds the members of $A$ that are not in $B$. 2. 'Not in $B$' is exactly the complement $B'$. 3. Requiring membership of both conditions at once is an intersection. 4. So $A-B=A\cap B'$. 5. Using a union instead would admit everything outside $B$, including elements that are not in $A$ at all. _Source: NECTA ACSEE 2022 Advanced Mathematics 142/1, Question 5: Sets_