How do I find the union and intersection using interval notation?

Question

D an E are sets how do I write the union and intersection using interval notation for D={vlv<1}E={vlv>=9} please help me understand this?

Answer 1

D is all numbers less than one D: (-∞, 1) and E is the set of all numbers greater than or equal to nine. E: [9,∞)

Interval notation is writing the solution set in brackets. A square bracket [ ] when we want to include the end value, or ( ) a round bracket when we don't.

 

The union, is the set of all combined values. Values in the set D or E., since there's a gap is just:

D∪E = (-∞, 1) ∪ [9,∞)

 

The intersection, is the set of all values they share. Values in both sets D and E. The set's D and E do not share any numbers so you get the empty set.

D∩E = { } or written as ∅