# Union and Intersection of intervals

I have two sets $A = \{1 \leq x \leq 5\}$ and $B = \{5 \leq x \leq 8\}$. Now I want to find the Union and Intersection of $A$ and $B$.

I tried Union[A, B], I got {1 <= x <= 5, 5 <= x <= 8} and for Intersection[A, B], I got {}. The correct answer for $A \cup B$ is [1, 8] and $A \cap B$ is {5}. How do I tell Mathematica to do that?

And if $A = \{1 < x < 5\}$ and $B = \{x > 5\}$. Now I want to find the Union and Intersection of $A$ and $B$. How do I tell Mathematica to do that?

• You will want to use Interval. – DavidC Oct 1 '12 at 1:13

a = Interval[{1, 5}];
b = Interval[{5, 8}];
IntervalUnion[a, b]


Interval[{1, 8}]

IntervalIntersection[a, b]


Interval[{5, 5}]

• Interval[{1,5},{5,8}] also gives IntervalUnion[a,b] (+1) – kglr Oct 1 '12 at 1:28
• Nice. I wasn't aware of that. – DavidC Oct 1 '12 at 1:30
• If A = {1 < x < 5} and B = {x > 1}. How must I do? – minthao_2011 Oct 1 '12 at 1:45
• @minthao: B = Interval[{1, ∞}]. – J. M. will be back soon Oct 1 '12 at 1:52
• @minthao. Mathematica seems to work only with closed intervals. Interval[{1,5] includes the numbers 1 and 5, and therefore does not match your original inequality, 1<x<5. I don't know whether there is a way to not include the end points. Perhaps this is a question worth asking. – DavidC Oct 1 '12 at 2:31