Write the following as intervals:

(i) {xx ∈ R, –4 < x ≤ 6}

(ii) {xx ∈ R, –12 < x < –10}

(iii) {xx ∈ R, 0 ≤ x < 7}

(iv) {xx ∈ R, 3 ≤ x ≤ 4}

Asked by Pragya Singh | 11 months ago |  77

##### Solution :-

(i) Given that,

{x∈ R, –4 < x ≤ 6}

To write the above expression as intervals 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 $$[a,b]$$

{x∈ R, –4 < x ≤ 6}  = (–4, 6]

(ii) Given that,

{x∈ R, –12 < x < –10} = (–12, –10)

To write the above expression as intervals 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 $$[a,b]$$

(iii) Given that,

{x∈ R, 0 ≤ x < 7}

To write the above expression as intervals 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 $$[a,b]$$

{x∈ R, 0 ≤ x < 7}  = [0, 7)

(iv) Given that,

{x∈ R, 3 ≤ x ≤ 4}

To write the above expression as intervals 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 $$[a,b]$$

{x∈ R, 3 ≤ x ≤ 4}  = [3, 4]

Answered by Abhisek | 11 months ago

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