Question

Write the set of points from -4 to 3 but excluding -1 and 3 as a union of intervals

Answer 1

The set of points from -4 to 3, excluding -1 and 3, is represented by the union of two intervals, written as (-4, -1) ∪ (-1, 3) in interval notation.

Step-by-step explanation:

To represent the set of points from -4 to 3, excluding -1 and 3, we can use a union of intervals. We break this down into parts where each interval represents a portion of the set without including the points we want to exclude (-1 and 3).

The first interval goes from -4 up to, but not including, -1. This is written in interval notation as (-4, -1). The second part starts just after -1 and goes up to, but not including, 3. This is written as (-1, 3). Notice that we use parentheses ( ) to indicate that the endpoints are not included in the intervals.

Therefore, the complete set of points from -4 to 3, excluding -1 and 3 as a union of intervals, is:

(-4, -1) ∪ (-1, 3)

Here, the symbol ∪ stands for the 'union' of the two intervals.

Answer 2

In this question, we have to write a set of points from -4 to 3 but excluding -1 and 3 as a union of intervals .

Set of points from -4 to 3 can be written as

`[-4,3 ]`

But we need to exclude -1 and 3 and write the final answer in union of sets .

So we put -1 and 3 in the intervals and put () with these numbers, that is

`[-4,-1)U(-1,3)`

And that's the final answer .