Write the following intervals in set-builder form:

Question 17 of 47beginner🔧 ApplyVery Short2 marks

(i)

(–3, 0)

Answer

{x : x ∈ R, –3 < x < 0}

(ii)

[6, 12]

Answer

{x : x ∈ R, 6 $\leq$ x $\leq$ 12}

(iii)

(6, 12]

Answer

{x : x ∈ R, 6 < x $\leq$ 12}

(iv)

[–23, 5)

Answer

{x : x ∈ R, –23 $\leq$ x < 5}

Explanation

To convert intervals to set-builder form, we need to identify the type of bracket used. Round brackets ( ) indicate strict inequality (< or >), meaning the endpoint is NOT included. Square brackets [ ] indicate non-strict inequality ( $\leq$ or $\geq$ ), meaning the endpoint IS included. For example, the interval [-3, 5) from the textbook is written as {x : -3 $\leq$ x < 5}, where the left endpoint is included and the right endpoint is excluded.

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