Question

What is the union of the two intervals (2,3] and [3,4], written as a single interval?

Answer 1

The union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].

What is an interval?

⇒ An interval is an expression that involves a subset of numbers on the actual line. These intervals contain all the actual numbers between the two numbers in the interval.

There are three types of intervals, these are:

1. Open intervals: are the numbers of the set between two numbers. These are denoted by a parenthesis (a,b), where a and b are any two numbers, and on the actual line, they are identified by an unfilled circle.
2. Closed intervals: are the sets formed by two numbers and those between them. This interval is denoted by square brackets [a,b], and on the actual line, it is identified by two filled circles for each number in the interval.
3. Semi-open interval: these intervals can be opened on the right and closed on the left (a,b] or opened on the left and closed on the right [a,b).

⇒ The intervals can be joined if in the math problem the result is between one end of the real line and the other end of the real line. There are two intervals with the sign of union in the middle of them.

The representation of the union of these intervals is given as follows:(2,3]∪[3,4]  , the union is denoted by ∪

Now as in every interval the three is part, we can express this union of this set as one in the following way:

⇒ (2,4]

Hence, the union of the two intervals (2,3] and [3,4], written as a single interval is (2,4].

Learn more about the union of sets here :

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