Intersection Math Example 2

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

medium

Let

A = \{x \in \mathbb{R} : x \ge 1\}

and

B = \{x \in \mathbb{R} : x \le 4\}

. Find

A \cap B

1
Rewrite each set in interval notation: $A = \{x \in \mathbb{R} : x \ge 1\} = [1, \infty)$ and $B = \{x \in \mathbb{R} : x \le 4\} = (-\infty, 4]$ .
2
The intersection requires both conditions to hold simultaneously: $x \ge 1$ AND $x \le 4$ , which means $1 \le x \le 4$ .
3
In interval notation, $A \cap B = [1, 4]$ . Geometrically, this is the overlap of the two rays on the number line.