Union Math Example 2

Follow the full solution, then compare it with the other examples linked below.

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Let

A = \{x \in \mathbb{R} : x > 2\}

and

B = \{x \in \mathbb{R} : x < 5\}

. Express

A \cup B

in interval notation.

1
In interval notation: $A = (2, \infty)$ and $B = (-\infty, 5)$ .
2
Since every real number is either greater than 2, less than 5, or both, $A \cup B$ covers the entire real line.
3
Therefore $A \cup B = (-\infty, \infty) = \mathbb{R}$ .

Answer

A \cup B = \mathbb{R}

When two intervals overlap and their union spans all real numbers, the result is

\mathbb{R}

. Visualising these sets on a number line makes this clear.

About Union

The union of sets $A$ and $B$ is the set of all elements that belong to $A$ , to $B$ , or to both, written $A \cup B$ .

Let [formula] and [formula]. Find [formula].

Let [formula] and [formula]. Find [formula].

Find [formula] if [formula] and [formula].