Question

Consider each of the following compound sentences:

x < 1 and x > -1 x < 1 or x > ????1
Does the change of the word from "and" to "or" change the solution set?
Use number line graphs to support your answer.

Answer 1

Yes, see explanation below.

Explanation:

First let's solve the first inequality:

x < 1 and x > -1

This means that x needs to fulfill these two inequalities at the same time, therefore, the solution set will be:

-1 < x < 1

The graphic is below and it is the interval (-1,1)

On the other hand the other inequality is

x< 1 or x > -1

So x should fulfill any of these two conditions and the solution set is the interval ( -∞, 1) ∪ (-1, +∞) which is all the real numbers (-∞, +∞)

The graphic line will be all Real numbers

The "and" means we're looking for the intersection of the solution sets. The "or" means we're looking for the union of the solution sets. So, yes, the use of these words change the solution set