Operations on Open and Closed Interval
The operations on open and closed intervals are:
- Union
- Intersection
- Complement
Union of Intervals
The union of two intervals P and Q contains all the elements present in one or both the intervals.
Examples
Some examples of union of two intervals are given below.
- (2, 7) ∪ (4, 9) = (2, 9)
- [1, 10] ∪ [5, 15] = [1, 15]
- (5, 12) ∪ [6, 14] = (5, 14]
Intersection of Intervals
The intersection of two intervals P and Q contains the elements present in both the intervals.
Examples
Some examples of union of two intervals are given below.
- (2, 7) ∩ (4, 9) = (4, 7)
- [1, 10] ∩ [5, 15] = [5, 10]
- (5, 12) ∩ [8, 14] = [8, 12)
Complement of Interval
The complement of interval contains the elements that are not included in the interval.
Examples
Some examples of complement of interval are given below.
- X = [3, 6] then, X’ = (-∞, 3) ∪ (6, ∞)
- Y = (4, 11) then, Y’ = (-∞, 4] ∪ [11, ∞)
Open Interval and Closed Interval
A closed interval includes its endpoints and is enclosed under square brackets. An open interval does not include its endpoints and is enclosed under parenthesis. In this article, we will explore the difference between an open interval and a closed interval, along with the open interval and closed interval definitions. Let’s start our learning on the topic “Difference Between an Open Interval and a Closed Interval”.
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