# Please, help me understand how these interval problems are solved

## Homework Statement

simplify:

1. (-∞, -2) ∩ [-2, ∞)

2. (-∞, 5] ∩ [5, ∞)

3. (-∞, 5) U (4, ∞)

4. (-∞, 5) ∩ (3, ∞)

## The Attempt at a Solution

It has been so long since I last saw a problem set like that. Honestly, I don't even remember how these problems should be solved. The text I am using just gives the definition and quickly glosses over since intervals are not the primary aim of it.
Would someone be so kind as to explain how I should go about solving these problems. Many thanks.

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Mark44
Mentor

## Homework Statement

simplify:

1. (-∞, -2) ∩ [-2, ∞)
The ∩ symbol means "intersect," which means the numbers that belong to both intervals. What numbers are less than -2 AND greater than or equal to -2?

Another approach is to draw the two intervals on the number line, to see which numbers are in both intervals.
2. (-∞, 5] ∩ [5, ∞)

3. (-∞, 5) U (4, ∞)
The U symbol means "union," which means the numbers that are in the first interval OR are in the second interval. A number belongs to the union of two intervals if it is in either or both intervals.
4. (-∞, 5) ∩ (3, ∞)

## The Attempt at a Solution

It has been so long since I last saw a problem set like that. Honestly, I don't even remember how these problems should be solved. The text I am using just gives the definition and quickly glosses over since intervals are not the primary aim of it.
Would someone be so kind as to explain how I should go about solving these problems. Many thanks.

NascentOxygen
Staff Emeritus
$\small(-\infty,-2)\normalsize\:\bigcap\; \small{[-2,\infty)}$