Can someone explain the meaning of $\setminus$ in operations with sets?

Question

I have never faced with such operator... what does '$\setminus$' mean? Does this expression make any sense? $(A \cup B) \setminus C = A \cup (B \setminus C)$

Answer 1

In the context of sets, that operation is set difference.

It is defined as: $$x\in A\backslash B \iff{} x \in \{t\, | \, t\in A \land t \notin B\}.$$

So, if we have the sets $A = \{1, 2, 3\}$ and $B = \{2, 3, 5\}$, then $A\backslash B = \{1\}$.

Note: Another notation for set difference is $A - B$.

Answer 2

It means that you subtract C from the combination of A and B

Answer 3

The $\setminus$ operand is called set difference. $X\setminus Y$ is defined to be the set which is comprised of elements in $X$ that are not in $Y$. For example, if $X = \{1,2,3,4\}$ and $Y = \{0,1,2\}$, then $X\setminus Y$ is the set of elements in $X$ which are not in $Y$. $1$ and $2$ appear in both $X$ and $Y$ so we remove these elements and we are left with $\{3,4\}$, giving $X\setminus Y = \{3,4\}$.

Answer 4

It means set subtraction...all the things that are in the set to the left but NOT in the set to the right. An equivallent definition is $X \setminus Y=X\cap Y^C$ Your equality is false. The left hand side says things that are in A or B, but not C.

The right hand side says things in A or (In B but not C)

So nothing from C can be in the left hand side, but things from C that happen to be in A can be on the right hand side, if that makes sense?