1. ## Sets

Is there any direct formula to find the complement of (A-B)?

2. Originally Posted by matsci0000
Is there any direct formula to find the complement of (A-B)?
(complement of A) union (A intersect B)

3. ## Complement of (A - B)

Hello matsci0000
Originally Posted by matsci0000
Is there any direct formula to find the complement of (A-B)?
A slightly simpler version of the formula that HallsofIvy has given you is $A' \cup B$, where $A'$ is the complement of $A$ (which is sometimes written $A^c$).

If you know the Laws of Sets, you can prove this as follows:

First, the definition: $A - B = A \cap B'$ (the elements that are in $A$ but not in $B$)

So $(A-B)' = (A \cap B')'$

$= A' \cup (B')'$ (De Morgan's Law)

$= A' \cup B$ (Involution Law)

4. Thanks, Grandad, I didn't take the time to simplify.