Please, help me understand how these interval problems are solved

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Homework Statement

simplify:

1. (-∞, -2) ∩ [-2, ∞)

2. (-∞, 5] ∩ [5, ∞)

3. (-∞, 5) U (4, ∞)

4. (-∞, 5) ∩ (3, ∞)

Homework Equations

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.

 

[Mark44]

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, ∞)

Homework Equations

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]

\small(-\infty,-2)\normalsize\:\bigcap\; \small{[-2,\infty)}

An open interval has its end point denoted by a round parenthesis: (

A closed interval has its end point denoted by a square bracket: [

Forgotten all this? Google is your best lead for on-line resources. Here's a start: http://www.sosmath.com/algebra/inequalities/ineq02/ineq02.html