# Simple Set Operation

1. Oct 1, 2007

### Steverino777

1. The problem statement, all variables and given/known data
Let U= all real numbers, A=[2,9), B=(0,1], C=[-1,4]. Express in interval notation: (A union B) - C

2. Relevant equations
A union B includes all elements that are in either A or B, including any objects that happen to lie in both A and B.

The difference A - B consists of all objects that are elements of A and are not elemnts of B

3. The attempt at a solution

I think the interval is from (4,9). A union B would be (0,1]union[2,9], then you remove from [-1, 4]. The only reason why I don't know if I'm right is because of the gap in the union of A and B. I don't know if that has any effect on the answer.

If (4,9) is correct then would it be safe to assume that (A union B) - C = A-C ?

2. Oct 1, 2007

### CompuChip

Your reasoning is correct.
Indeed in this case, $$(A \cup B) - C = A - C$$, because B is completely contained within C. So whatever elements from B you add to A when taking the union, you take them out again when removing C.
Of course, this is in general not true (e.g. A = [0, 1], B = [1, 2], C = [0, 1/2) is a counter example).

The gap in the union doesn't matter: X - Y is defined as the set of all elements which are in X but not in Y.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?