How to remember various set operations very easily?

Question

I need an way to remember the set operations very easily.

Does anybody have any idea?

For example, how do you remember the distinction between Set-Intersection and Set-difference? I regularly mess it up.

Answer 1

As 5xum mentioned in the comments, union starts with a u and has a symbol $\cup$ that looks very much like a $u$. Then intersection is simply the same symbol flipped $\cap$.

As for what they mean, you can think of union $A \cup B$ as a cup (indeed, the LaTeX command for it is \cup) in which you pour all of the elements of both $A$ and $B$, whereas $A \cap B$ has two legs, one in $A$ and one in $B$, so it contains only those elements that are in both $A$ and $B$.

Answer 2

The trick I used to memorize them actually stemmed from formal logic (which you may or may not have had any exposure to):

The symbol $\land$ is a way to symbolize the binary connective "and". Notice it looks like a "pointy" $\cap$. Similarly $\lor$ (or) looks similar to $\cup$.

Now, $$x\in A\cap B$$ can be read as $$x\text{ is in } A \textbf{ and } B$$ and $$x\in A\cup B$$ is $$x\text{ is in } A \textbf{ or } B$$

This might actually be why the symbols look similar, actually.