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Sagot :
The complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
According to the given question.
We have an interval [2, 3).
Let A = [2, 3)
Which is defined as
[2, 3) = {x ∈ r : 2 ≤ x < 3}
This means that the interval [2, 3) contains all the real numbers which are greater and equal to 2 and less than 3.
And, here it is also given that the universal set is r ( set of real numbers).
As we know that " the complement of an interval is a set A of real numbers that conatins all the elements of universal set U except the number that lying between the given two numbers in the inerval" i.e.
[tex]A^{c} = U - A[/tex]
Where,
[tex]A^{c}[/tex] is the complement of interval A
Thereofre, the complement of the given interval [2, 3) will be all the elements of universal set i.e real numbers except 2 and the real numbers which lies in between 2 and 3.
So, we can say that
[tex]A^{c} = (-\infty, 2) \cup(3, \infty)[/tex]
Where, [tex]A^{c}[/tex] is the complement of the interval A.
Hence, the complement of the interval [2, 3) is ( -∞, 2) ∪ (3, ∞).
Find out more information about complement of an interval here:
https://brainly.com/question/13202631
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