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QuestionExpress the set {x∣x<1 or x≥13}\{x \mid x<1 \text{ or } x \geq 13\} in interval notation.

Studdy Solution

STEP 1

Assumptions1. We are given a set of numbers defined by the conditions x<1x<1 or x≥13x \geq13. . We need to express this set in interval notation.

STEP 2

Interval notation is a way of writing subsets of the real number line. An interval is written as a pair of numbers, with the smaller number first, and the larger number second. The numbers are separated by a comma, and the pair is enclosed in either parentheses or brackets, depending on whether the endpoints are included in the interval.

STEP 3

The first condition is x<1x<1. This means all numbers less than1 are included in the set. In interval notation, this is expressed as (−∞,1)(-\infty,1).
x<1→(−∞,1)x<1 \rightarrow (-\infty,1)

STEP 4

The second condition is x≥13x \geq13. This means all numbers greater than or equal to13 are included in the set. In interval notation, this is expressed as [13,∞)[13, \infty).
x≥13→[13,∞)x \geq13 \rightarrow [13, \infty)

STEP 5

Since the set includes all numbers that satisfy either condition, we combine the two intervals using the union symbol ∪\cup.
(−∞,1)∪[13,∞)(-\infty,1) \cup [13, \infty)This is the set expressed in interval notation.

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