Write the following intervals in set-builder form:

(i) (–3, 0)

(ii) [6, 12]

(iii) (6, 12]

(iv) [–23, 5)

Asked by Pragya Singh | 11 months ago |  60

##### Solution :-

(i) (–3, 0)

To write the above interval in set builder form The set of real numbers $$\{y : a < y< b\}$$ is called an open interval and is denoted by (a,b) . The interval which contains the end points also is called close interval and is denoted by $$[a,b]$$

(–3, 0)  = {x∈ R, –3 < x < 0}

(ii) [6, 12]

To write the above interval in set builder form The set of real numbers $$\{y : a < y< b\}$$ is called an open interval and is denoted by (a,b) . The interval which contains the end points also is called close interval and is denoted by $$[a,b]$$

[6, 12]  = {x∈ R, 6 ≤ x ≤ 12}

(iii) (6, 12]

To write the above interval in set builder form The set of real numbers $$\{y : a < y< b\}$$ is called an open interval and is denoted by (a,b) .The interval which contains the end points also is called close interval and is denoted by $$[a,b]$$

(6, 12]  ={x∈ R, 6 < x ≤ 12}

(iv) [–23, 5)

To write the above interval in set builder form The set of real numbers $$\{y : a < y< b\}$$ is called an open interval and is denoted by (a,b) .The interval which contains the end points also is called close interval and is denoted by $$[a,b]$$

[–23, 5)  = {x∈ R, –23 ≤ x < 5}

Answered by Abhisek | 11 months ago

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