Question

Consider the interval [2, 3) = {x € r : 2 <= x < 3}. Find the complement of this interval where the universal set is taken to be r, the set of real numbers.

Answer 1

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.

$A^{c} = U - A$

Where,

$A^{c}$ 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

$A^{c} = (-\infty, 2) \cup(3, \infty)$

Where, $A^{c}$ 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:

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