Why is the multiplication of two sets their intersection, and the addition their union? Why is the multiplication of two sets their intersection, and the addition their union? e.g.
$$\{a,b,c\} + \{c,d,e\} = \{a,b,c,d,e\}$$
$$\{a,b,c\} * \{c,d,e\} = \{c\}$$
I don't know if this is true, but in an exercise, it was defined this way.
 A: 
I don't know if this is true, but in an exercise, it was defined this way.

If it's defined that way, then it's true, of course.
The notation is not widespread used, though.  What makes the notation a poor choice is that

*

*There is already a short and established way to write intersections and unions, namely $A\cup B$ and $A\cap B$ for uniion and intersection, respectively.


*The notation is usually interpreted in a different way similar to when you apply a function to all elements of a set one writes $$f(A) := \{f(a)\mid a\in A\}$$ and similarly for a binary operation $\circ$ that operates on elments of $A$ and $B$: $$A\circ B := \{a\circ b\mid a\in A, b\in B\}$$
Using convention 2, the semantics of the expressions would be:
$$\{a,b,c\} \circ \{c,d,e\} = \{a\circ c, a\circ d, a\circ e, b\circ c,b\circ d,b\circ e,c\circ c,c\circ d,c\circ e\}$$
where $\circ$ is one of $+$ or $*$.
One reason for using $*\equiv\cap$ and $+\equiv\cup$ migh be for typographic reasons when there is no terminal or keypord that can represent or input symbols ∩ and ∪.
