Question

Write the set of points from -5 to 4 but excluding -1 and 4 as a union of intervals

Answer 1

We need to write interval for the number from -5 to 4.

We need to exclude numbers -1 and 4 from it.

First we need to note some important points about interval notation.

We need to check, which numbers are included and which numbers are excluded in the given interval.

We use open-interval ( or ) for excluded values and [ or ] close-interval for included values.

For the given problem, we have given three numbers: -5, -1 and 4.

It's clarly given that -1 and 4 are not included. But it is not said that -5 is excluded, so -5 is included number.

-1 comes in between -5 and 4 on the number line.

So let us write interval notation from -5 to -1. (Note : -5 is included and -1 excluded).

Therefore, we will write close interval " [ " on left side of -5 and an open interval " ( "on right side of -1. We get,

[-5 , -1 ).

Now, we will write interval notation from -1 to 4.

Both are excluced values, so we will take open intervals ( ) on left and right side of -1 and 4.

So, we get another part of the interval as

(-1,4).

We will put union symbol in between above two interval notations we get.

Therefore, final interval notation is

[-5 , -1 ) ∪ (-1,4).