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Mathematics

Set-builder form of set A = {12,23,34}\Big{\dfrac{1}{2}, \dfrac{2}{3}, \dfrac{3}{4}\Big} is :

  1. {x=nn+1,n∈N and n>1}{\Big{x = \dfrac{n}{n + 1}, n ∈ N \text{ and } n > 1\Big}}

  2. {x=n−1n−2,n∈N and n>2}{\Big{x = \dfrac{n - 1}{n - 2}, n ∈ N \text{ and } n > 2\Big}}

  3. {x=nn+1,n∈N and 1<n<2}{\Big{x = \dfrac{n}{n + 1}, n ∈ N \text{ and } 1 < n < 2\Big}}

  4. {x=nn+1,n∈N and 1≤n<4}{\Big{x = \dfrac{n}{n + 1}, n ∈ N \text{ and } 1 ≤ n < 4\Big}}

Sets

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Answer

set A = {12,23,34}\Big{\dfrac{1}{2}, \dfrac{2}{3}, \dfrac{3}{4}\Big}

= {11+1,22+1,33+1}\Big{\dfrac{1}{1 + 1}, \dfrac{2}{2 + 1}, \dfrac{3}{3 + 1}\Big}

= {x=nn+1,n∈N and 1≤n<4}{\Big{x = \dfrac{n}{n + 1}, n ∈ N \text{ and } 1 ≤ n < 4\Big}}

Hence, option 4 is the correct option.

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