# Thread: Logical expression for set

1. ## Logical expression for set

I don't know the logical expression for $\{x \in B|x \not \in C\}$.

I am thinking it could be one of these:

$\forall x(x \not \in c \rightarrow x \in B)$

or

$\forall x(x \in B \wedge x \not \in C)$

or
$
\forall x \in B (x \not C)$

Could you help?

2. {x in B | x not in C} is the set of all x such that x is in B and x is not in C.

That is, for all x, we have x in {x in B | x not in C} if and only if (x is in B and x is not in C).

Put another way, {x in B | x not in C} = B\C, where '\' stands for relative complement.

3. Originally Posted by novice
I don't know the logical expression for $\{x \in B|x \not \in C\}$.
$\forall x(x \in B \wedge x \not \in C)$
$\{x \in B|x \not \in C\}=B\setminus C$.